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Vector Symbolic Architecture (VSA) is emerging in machine learning due to its efficiency, but they are hindered by issues of hyperdimensionality and accuracy. As a promising mitigation, the Low-Dimensional Computing (LDC) method significantly reduces the vector dimension by ~100 times while maintaining accuracy, by employing a gradient-based optimization. Despite its potential, LDC optimization for VSA is still underexplored. Our investigation into vector updates underscores the importance of stable, adaptive dynamics in LDC training. We also reveal the overlooked yet critical roles of batch normalization (BN) and knowledge distillation (KD) in standard approaches. Besides the accuracy boost, BN does not add computational overhead during inference, and KD significantly enhances inference confidence. Through extensive experiments and ablation studies across multiple benchmarks, we provide a thorough evaluation of our approach and extend the interpretability of binary neural network optimization similar to LDC, previously unaddressed in BNN literature., Comment: 10 pages, 2 figures. Accepted in CPAL 2025

Water infrastructures are essential for drinking water supply, irrigation, fire protection, and other critical applications. However, water pumping systems, which are key to transporting water to the point of use, consume significant amounts of energy and emit millions of tons of greenhouse gases annually. With the wide deployment of digital water meters and sensors in these infrastructures, Machine Learning (ML) has the potential to optimize water supply control and reduce greenhouse gas emissions. Nevertheless, the inherent vulnerability of ML methods in terms of worst-case performance raises safety concerns when deployed in critical water infrastructures. To address this challenge, we propose a learning-augmented online control algorithm, termed LAOC, designed to dynamically schedule the activation and/or speed of water pumps. To ensure safety, we introduce a novel design of safe action sets for online control problems. By leveraging these safe action sets, LAOC can provably guarantee safety constraints while utilizing ML predictions to reduce energy and environmental costs. Our analysis reveals the tradeoff between safety requirements and average energy/environmental cost performance. Additionally, we conduct an experimental study on a building water supply system to demonstrate the empirical performance of LAOC. The results indicate that LAOC can effectively reduce environmental and energy costs while guaranteeing safety constraints., Comment: Accepted by e-Energy 2025

The skyrocketing demand for artificial intelligence (AI) has created an enormous appetite for globally deployed power-hungry servers. As a result, the environmental footprint of AI systems has come under increasing scrutiny. More crucially, the current way that we exploit AI workloads' flexibility and manage AI systems can lead to wildly different environmental impacts across locations, increasingly raising environmental inequity concerns and creating unintended sociotechnical consequences. In this paper, we advocate environmental equity as a priority for the management of future AI systems, advancing the boundaries of existing resource management for sustainable AI and also adding a unique dimension to AI fairness. Concretely, we uncover the potential of equity-aware geographical load balancing to fairly re-distribute the environmental cost across different regions, followed by algorithmic challenges. We conclude by discussing a few future directions to exploit the full potential of system management approaches to mitigate AI's environmental inequity., Comment: Accepted by Communications of the ACM. All the authors contributed equally and are listed in alphabetical order of last name

The surging demand for AI has led to a rapid expansion of energy-intensive data centers, impacting the environment through escalating carbon emissions and water consumption. While significant attention has been paid to AI's growing environmental footprint, the public health burden, a hidden toll of AI, has been largely overlooked. Specifically, AI's lifecycle, from chip manufacturing to data center operation, significantly degrades air quality through emissions of criteria air pollutants such as fine particulate matter, substantially impacting public health. This paper introduces a methodology to model pollutant emissions across AI's lifecycle, quantifying the public health impacts. Our findings reveal that training an AI model of the Llama3.1 scale can produce air pollutants equivalent to more than 10,000 round trips by car between Los Angeles and New York City. The total public health burden of U.S. data centers in 2030 is valued at up to more than $20 billion per year, double that of U.S. coal-based steelmaking and comparable to that of on-road emissions of California. Further, the public health costs unevenly impact economically disadvantaged communities, where the per-household health burden could be 200x more than that in less-impacted communities. We recommend adopting a standard reporting protocol for criteria air pollutants and the public health costs of AI, paying attention to all impacted communities, and implementing health-informed AI to mitigate adverse effects while promoting public health equity., Comment: 29 pages

AI computing and data centers consume a large amount of freshwater, both directly for cooling and indirectly for electricity generation. While most attention has been paid to developed countries such as the U.S., this paper presents the first-of-its-kind dataset that combines nation-level weather and electricity generation data to estimate water usage efficiency for data centers in 41 African countries across five different climate regions. We also use our dataset to evaluate and estimate the water consumption of inference on two large language models (i.e., Llama-3-70B and GPT-4) in 11 selected African countries. Our findings show that writing a 10-page report using Llama-3-70B could consume about \textbf{0.7 liters} of water, while the water consumption by GPT-4 for the same task may go up to about 60 liters. For writing a medium-length email of 120-200 words, Llama-3-70B and GPT-4 could consume about \textbf{0.13 liters} and 3 liters of water, respectively. Interestingly, given the same AI model, 8 out of the 11 selected African countries consume less water than the global average, mainly because of lower water intensities for electricity generation. However, water consumption can be substantially higher in some African countries with a steppe climate than the U.S. and global averages, prompting more attention when deploying AI computing in these countries. Our dataset is publicly available on \href{https://huggingface.co/datasets/masterlion/WaterEfficientDatasetForAfricanCountries/tree/main}{Hugging Face}., Comment: Accepted by NeurIPS 2024 Workshop on Tackling Climate Change with Machine Learning

The combination of the Bayesian game and learning has a rich history, with the idea of controlling a single agent in a system composed of multiple agents with unknown behaviors given a set of types, each specifying a possible behavior for the other agents. The idea is to plan an agent's own actions with respect to those types which it believes are most likely to maximize the payoff. However, the type beliefs are often learned from past actions and likely to be incorrect. With this perspective in mind, we consider an agent in a game with type predictions of other components, and investigate the impact of incorrect beliefs to the agent's payoff. In particular, we formally define a tradeoff between risk and opportunity by comparing the payoff obtained against the optimal payoff, which is represented by a gap caused by trusting or distrusting the learned beliefs. Our main results characterize the tradeoff by establishing upper and lower bounds on the Pareto front for both normal-form and stochastic Bayesian games, with numerical results provided., Comment: 26 pages, NeurIPS 2024

Online Budgeted Matching (OBM) is a classic problem with important applications in online advertising, online service matching, revenue management, and beyond. Traditional online algorithms typically assume a small bid setting, where the maximum bid-to-budget ratio (\kappa) is infinitesimally small. While recent algorithms have tried to address scenarios with non-small or general bids, they often rely on the Fractional Last Matching (FLM) assumption, which allows for accepting partial bids when the remaining budget is insufficient. This assumption, however, does not hold for many applications with indivisible bids. In this paper, we remove the FLM assumption and tackle the open problem of OBM with general bids. We first establish an upper bound of 1-\kappa on the competitive ratio for any deterministic online algorithm. We then propose a novel meta algorithm, called MetaAd, which reduces to different algorithms with first known provable competitive ratios parameterized by the maximum bid-to-budget ratio \kappa \in [0, 1]. As a by-product, we extend MetaAd to the FLM setting and get provable competitive algorithms. Finally, we apply our competitive analysis to the design learning-augmented algorithms., Comment: Accepted by NeurIPS 2024

Public models offer predictions to a variety of downstream tasks and have played a crucial role in various AI applications, showcasing their proficiency in accurate predictions. However, the exclusive emphasis on prediction accuracy may not align with the diverse end objectives of downstream agents. Recognizing the public model's predictions as a service, we advocate for integrating the objectives of downstream agents into the optimization process. Concretely, to address performance disparities and foster fairness among heterogeneous agents in training, we propose a novel Equitable Objective. This objective, coupled with a policy gradient algorithm, is crafted to train the public model to produce a more equitable/uniform performance distribution across downstream agents, each with their unique concerns. Both theoretical analysis and empirical case studies have proven the effectiveness of our method in advancing performance equity across diverse downstream agents utilizing the public model for their decision-making. Codes and datasets are released at https://github.com/Ren-Research/Socially-Equitable-Public-Models., Comment: Accepted by the ICML 2024

Text watermarks for large language models (LLMs) have been commonly used to identify the origins of machine-generated content, which is promising for assessing liability when combating deepfake or harmful content. While existing watermarking techniques typically prioritize robustness against removal attacks, unfortunately, they are vulnerable to spoofing attacks: malicious actors can subtly alter the meanings of LLM-generated responses or even forge harmful content, potentially misattributing blame to the LLM developer. To overcome this, we introduce a bi-level signature scheme, Bileve, which embeds fine-grained signature bits for integrity checks (mitigating spoofing attacks) as well as a coarse-grained signal to trace text sources when the signature is invalid (enhancing detectability) via a novel rank-based sampling strategy. Compared to conventional watermark detectors that only output binary results, Bileve can differentiate 5 scenarios during detection, reliably tracing text provenance and regulating LLMs. The experiments conducted on OPT-1.3B and LLaMA-7B demonstrate the effectiveness of Bileve in defeating spoofing attacks with enhanced detectability. Code is available at https://github.com/Tongzhou0101/Bileve-official., Comment: NeurIPS 2024 camera-ready

Freshwater scarcity is a global problem that requires collective efforts across all industry sectors. Nevertheless, a lack of access to operational water footprint data bars many applications from exploring optimization opportunities hidden within the temporal and spatial variations. To break this barrier into research in water sustainability, we build a dataset for operation direct water usage in the cooling systems and indirect water embedded in electricity generation. Our dataset consists of the hourly water efficiency of major U.S. cities and states from 2019 to 2023. We also offer cooling system models that capture the impact of weather on water efficiency. We present a preliminary analysis of our dataset and discuss three potential applications that can benefit from it. Our dataset is publicly available at Open Science Framework (OSF), Comment: Accepted by ACM e-Energy 2024

The sharply increasing sizes of artificial intelligence (AI) models come with significant energy consumption and environmental footprints, which can disproportionately impact certain (often marginalized) regions and hence create environmental inequity concerns. Moreover, concerns with social inequity have also emerged, as AI computing resources may not be equitably distributed across the globe and users from certain disadvantaged regions with severe resource constraints can consistently experience inferior model performance. Importantly, the inequity concerns that encompass both social and environmental dimensions still remain unexplored and have increasingly hindered responsible AI. In this paper, we leverage the spatial flexibility of AI inference workloads and propose equitable geographical load balancing (GLB) to fairly balance AI's regional social and environmental costs. Concretely, to penalize the disproportionately high social and environmental costs for equity, we introduce $L_q$ norms as novel regularization terms into the optimization objective for GLB decisions. Our empirical results based on real-world AI inference traces demonstrate that while the existing GLB algorithms result in disproportionately large social and environmental costs in certain regions, our proposed equitable GLB can fairly balance AI's negative social and environmental costs across all the regions., Comment: Presented at HotEthics 2024 (co-located with ASPLOS' 24)

Brain-Computer interfaces (BCIs) are typically designed to be lightweight and responsive in real-time to provide users timely feedback. Classical feature engineering is computationally efficient but has low accuracy, whereas the recent neural networks (DNNs) improve accuracy but are computationally expensive and incur high latency. As a promising alternative, the low-dimensional computing (LDC) classifier based on vector symbolic architecture (VSA), achieves small model size yet higher accuracy than classical feature engineering methods. However, its accuracy still lags behind that of modern DNNs, making it challenging to process complex brain signals. To improve the accuracy of a small model, knowledge distillation is a popular method. However, maintaining a constant level of distillation between the teacher and student models may not be the best way for a growing student during its progressive learning stages. In this work, we propose a simple scheduled knowledge distillation method based on curriculum data order to enable the student to gradually build knowledge from the teacher model, controlled by an $\alpha$ scheduler. Meanwhile, we employ the LDC/VSA as the student model to enhance the on-device inference efficiency for tiny BCI devices that demand low latency. The empirical results have demonstrated that our approach achieves better tradeoff between accuracy and hardware efficiency compared to other methods., Comment: Accepted as a full paper by the tinyML Research Symposium 2024

This paper studies online resource allocation with replenishable budgets, where budgets can be replenished on top of the initial budget and an agent sequentially chooses online allocation decisions without violating the available budget constraint at each round. We propose a novel online algorithm, called OACP (Opportunistic Allocation with Conservative Pricing), that conservatively adjusts dual variables while opportunistically utilizing available resources. OACP achieves a bounded asymptotic competitive ratio in adversarial settings as the number of decision rounds T gets large. Importantly, the asymptotic competitive ratio of OACP is optimal in the absence of additional assumptions on budget replenishment. To further improve the competitive ratio, we make a mild assumption that there is budget replenishment every T^* >= 1 decision rounds and propose OACP+ to dynamically adjust the total budget assignment for online allocation. Next, we move beyond the worst-case and propose LA-OACP (Learning-Augmented OACP/OACP+), a novel learning-augmented algorithm for online allocation with replenishable budgets. We prove that LA-OACP can improve the average utility compared to OACP/OACP+ when the ML predictor is properly trained, while still offering worst-case utility guarantees when the ML predictions are arbitrarily wrong. Finally, we run simulation studies of sustainable AI inference powered by renewables, validating our analysis and demonstrating the empirical benefits of LA-OACP., Comment: Accepted by ACM SIGMETRICS 2024

Training large-scale artificial intelligence (AI) models demands significant computational power and energy, leading to increased carbon footprint with potential environmental repercussions. This paper delves into the challenges of training AI models across geographically distributed (geo-distributed) data centers, emphasizing the balance between learning performance and carbon footprint. We consider Federated Learning (FL) as a solution, which prioritizes model parameter exchange over raw data, ensuring data privacy and compliance with local regulations. Given the variability in carbon intensity across regions, we propose a new framework called CAFE (short for Carbon-Aware Federated Learning) to optimize training within a fixed carbon footprint budget. Our approach incorporates coreset selection to assess learning performance, employs the Lyapunov drift-plus-penalty framework to address the unpredictability of future carbon intensity, and devises an efficient algorithm to address the combinatorial complexity of the data center selection. Through extensive simulations using real-world carbon intensity data, we demonstrate the efficacy of our algorithm, highlighting its superiority over existing methods in optimizing learning performance while minimizing environmental impact., Comment: Preprint, Experiments Updated

This paper studies the problem of Anytime-Competitive Markov Decision Process (A-CMDP). Existing works on Constrained Markov Decision Processes (CMDPs) aim to optimize the expected reward while constraining the expected cost over random dynamics, but the cost in a specific episode can still be unsatisfactorily high. In contrast, the goal of A-CMDP is to optimize the expected reward while guaranteeing a bounded cost in each round of any episode against a policy prior. We propose a new algorithm, called Anytime-Competitive Reinforcement Learning (ACRL), which provably guarantees the anytime cost constraints. The regret analysis shows the policy asymptotically matches the optimal reward achievable under the anytime competitive constraints. Experiments on the application of carbon-intelligent computing verify the reward performance and cost constraint guarantee of ACRL., Comment: Accepted by NeurIPS 2023

We study a challenging form of Smoothed Online Convex Optimization, a.k.a. SOCO, including multi-step nonlinear switching costs and feedback delay. We propose a novel machine learning (ML) augmented online algorithm, Robustness-Constrained Learning (RCL), which combines untrusted ML predictions with a trusted expert online algorithm via constrained projection to robustify the ML prediction. Specifically,we prove that RCL is able to guarantee$(1+\lambda)$-competitiveness against any given expert for any$\lambda>0$, while also explicitly training the ML model in a robustification-aware manner to improve the average-case performance. Importantly,RCL is the first ML-augmented algorithm with a provable robustness guarantee in the case of multi-step switching cost and feedback delay.We demonstrate the improvement of RCL in both robustness and average performance using battery management for electrifying transportationas a case study., Comment: Accepted by NeurIPS 2023

We study the tradeoff between consistency and robustness in the context of a single-trajectory time-varying Markov Decision Process (MDP) with untrusted machine-learned advice. Our work departs from the typical approach of treating advice as coming from black-box sources by instead considering a setting where additional information about how the advice is generated is available. We prove a first-of-its-kind consistency and robustness tradeoff given Q-value advice under a general MDP model that includes both continuous and discrete state/action spaces. Our results highlight that utilizing Q-value advice enables dynamic pursuit of the better of machine-learned advice and a robust baseline, thus result in near-optimal performance guarantees, which provably improves what can be obtained solely with black-box advice., Comment: 32 pages, NeurIPS 2023

Fueled by the soaring popularity of large language and foundation models, the accelerated growth of artificial intelligence (AI) models' enormous environmental footprint has come under increased scrutiny. While many approaches have been proposed to make AI more energy-efficient and environmentally friendly, environmental inequity -- the fact that AI's environmental footprint can be disproportionately higher in certain regions than in others -- has emerged, raising social-ecological justice concerns. This paper takes a first step toward addressing AI's environmental inequity by balancing its regional negative environmental impact. Concretely, we focus on the carbon and water footprints of AI model inference and propose equity-aware geographical load balancing (GLB) to explicitly address AI's environmental impacts on the most disadvantaged regions. We run trace-based simulations by considering a set of 10 geographically-distributed data centers that serve inference requests for a large language AI model. The results demonstrate that existing GLB approaches may amplify environmental inequity while our proposed equity-aware GLB can significantly reduce the regional disparity in terms of carbon and water footprints., Comment: Accepted by ACM e-Energy 2024

This paper studies decentralized online convex optimization in a networked multi-agent system and proposes a novel algorithm, Learning-Augmented Decentralized Online optimization (LADO), for individual agents to select actions only based on local online information. LADO leverages a baseline policy to safeguard online actions for worst-case robustness guarantees, while staying close to the machine learning (ML) policy for average performance improvement. In stark contrast with the existing learning-augmented online algorithms that focus on centralized settings, LADO achieves strong robustness guarantees in a decentralized setting. We also prove the average cost bound for LADO, revealing the tradeoff between average performance and worst-case robustness and demonstrating the advantage of training the ML policy by explicitly considering the robustness requirement., Comment: Accepted by SIGMETRICS 2025

Many problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but it lacks robustness and can perform arbitrarily poorly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judicious condition to hedge against future uncertainties, decides whether to follow the expert's decision or the RL decision for each online item. We prove that for any $\rho\in[0,1]$, LOMAR is $\rho$-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines. Our code is available at: https://github.com/Ren-Research/LOMAR, Comment: Accepted by ICML 2023

Online optimization with memory costs has many real-world applications, where sequential actions are made without knowing the future input. Nonetheless, the memory cost couples the actions over time, adding substantial challenges. Conventionally, this problem has been approached by various expert-designed online algorithms with the goal of achieving bounded worst-case competitive ratios, but the resulting average performance is often unsatisfactory. On the other hand, emerging machine learning (ML) based optimizers can improve the average performance, but suffer from the lack of worst-case performance robustness. In this paper, we propose a novel expert-robustified learning (ERL) approach, achieving {both} good average performance and robustness. More concretely, for robustness, ERL introduces a novel projection operator that robustifies ML actions by utilizing an expert online algorithm; for average performance, ERL trains the ML optimizer based on a recurrent architecture by explicitly considering downstream expert robustification. We prove that, for any $\lambda\geq1$, ERL can achieve $\lambda$-competitive against the expert algorithm and $\lambda\cdot C$-competitive against the optimal offline algorithm (where $C$ is the expert's competitive ratio). Additionally, we extend our analysis to a novel setting of multi-step memory costs. Finally, our analysis is supported by empirical experiments for an energy scheduling application., Comment: This paper has been accepted by and will be presented at the INFOCOM 2023

As a type of valuable intellectual property (IP), deep neural network (DNN) models have been protected by techniques like watermarking. However, such passive model protection cannot fully prevent model abuse. In this work, we propose an active model IP protection scheme, namely NNSplitter, which actively protects the model by splitting it into two parts: the obfuscated model that performs poorly due to weight obfuscation, and the model secrets consisting of the indexes and original values of the obfuscated weights, which can only be accessed by authorized users with the support of the trusted execution environment. Experimental results demonstrate the effectiveness of NNSplitter, e.g., by only modifying 275 out of over 11 million (i.e., 0.002%) weights, the accuracy of the obfuscated ResNet-18 model on CIFAR-10 can drop to 10%. Moreover, NNSplitter is stealthy and resilient against norm clipping and fine-tuning attacks, making it an appealing solution for DNN model protection. The code is available at: https://github.com/Tongzhou0101/NNSplitter., Comment: To appear at ICML 2023

The growing carbon footprint of artificial intelligence (AI) has been undergoing public scrutiny. Nonetheless, the equally important water (withdrawal and consumption) footprint of AI has largely remained under the radar. For example, training the GPT-3 language model in Microsoft's state-of-the-art U.S. data centers can directly evaporate 700,000 liters of clean freshwater, but such information has been kept a secret. More critically, the global AI demand is projected to account for 4.2-6.6 billion cubic meters of water withdrawal in 2027, which is more than the total annual water withdrawal of 4-6 Denmark or half of the United Kingdom. This is concerning, as freshwater scarcity has become one of the most pressing challenges. To respond to the global water challenges, AI can, and also must, take social responsibility and lead by example by addressing its own water footprint. In this paper, we provide a principled methodology to estimate the water footprint of AI, and also discuss the unique spatial-temporal diversities of AI's runtime water efficiency. Finally, we highlight the necessity of holistically addressing water footprint along with carbon footprint to enable truly sustainable AI., Comment: Accepted by Communications of the ACM. Source codes available at: https://github.com/Ren-Research/Making-AI-Less-Thirsty

Fast model updates for unseen tasks on intelligent edge devices are crucial but also challenging due to the limited computational power. In this paper,we propose MetaLDC, which meta-trains braininspired ultra-efficient low-dimensional computing classifiers to enable fast adaptation on tiny devices with minimal computational costs. Concretely, during the meta-training stage, MetaLDC meta trains a representation offline by explicitly taking into account that the final (binary) class layer will be fine-tuned for fast adaptation for unseen tasks on tiny devices; during the meta-testing stage, MetaLDC uses closed-form gradients of the loss function to enable fast adaptation of the class layer. Unlike traditional neural networks, MetaLDC is designed based on the emerging LDC framework to enable ultra-efficient on-device inference. Our experiments have demonstrated that compared to SOTA baselines, MetaLDC achieves higher accuracy, robustness against random bit errors, as well as cost-efficient hardware computation., Comment: Accepted as a full paper by the TinyML Research Symposium 2023; 8 pages, 5 figures

Online optimization with multiple budget constraints is challenging since the online decisions over a short time horizon are coupled together by strict inventory constraints. The existing manually-designed algorithms cannot achieve satisfactory average performance for this setting because they often need a large number of time steps for convergence and/or may violate the inventory constraints. In this paper, we propose a new machine learning (ML) assisted unrolling approach, called LAAU (Learning-Assisted Algorithm Unrolling), which unrolls the online decision pipeline and leverages an ML model for updating the Lagrangian multiplier online. For efficient training via backpropagation, we derive gradients of the decision pipeline over time. We also provide the average cost bounds for two cases when training data is available offline and collected online, respectively. Finally, we present numerical results to highlight that LAAU can outperform the existing baselines., Comment: Accepted by AAAI'23

Continual learning faces a crucial challenge of catastrophic forgetting. To address this challenge, experience replay (ER) that maintains a tiny subset of samples from previous tasks has been commonly used. Existing ER works usually focus on refining the learning objective for each task with a static memory construction policy. In this paper, we formulate the dynamic memory construction in ER as a combinatorial optimization problem, which aims at directly minimizing the global loss across all experienced tasks. We first apply three tactics to solve the problem in the offline setting as a starting point. To provide an approximate solution to this problem in the online continual learning setting, we further propose the Global Pseudo-task Simulation (GPS), which mimics future catastrophic forgetting of the current task by permutation. Our empirical results and analyses suggest that the GPS consistently improves accuracy across four commonly used vision benchmarks. We have also shown that our GPS can serve as the unified framework for integrating various memory construction policies in existing ER works., Comment: Accepted by the NeurIPS 2022

Malicious architecture extraction has been emerging as a crucial concern for deep neural network (DNN) security. As a defense, architecture obfuscation is proposed to remap the victim DNN to a different architecture. Nonetheless, we observe that, with only extracting an obfuscated DNN architecture, the adversary can still retrain a substitute model with high performance (e.g., accuracy), rendering the obfuscation techniques ineffective. To mitigate this under-explored vulnerability, we propose ObfuNAS, which converts the DNN architecture obfuscation into a neural architecture search (NAS) problem. Using a combination of function-preserving obfuscation strategies, ObfuNAS ensures that the obfuscated DNN architecture can only achieve lower accuracy than the victim. We validate the performance of ObfuNAS with open-source architecture datasets like NAS-Bench-101 and NAS-Bench-301. The experimental results demonstrate that ObfuNAS can successfully find the optimal mask for a victim model within a given FLOPs constraint, leading up to 2.6% inference accuracy degradation for attackers with only 0.14x FLOPs overhead. The code is available at: https://github.com/Tongzhou0101/ObfuNAS., Comment: 9 pages

By integrating domain knowledge with labeled samples, informed machine learning has been emerging to improve the learning performance for a wide range of applications. Nonetheless, rigorous understanding of the role of injected domain knowledge has been under-explored. In this paper, we consider an informed deep neural network (DNN) with over-parameterization and domain knowledge integrated into its training objective function, and study how and why domain knowledge benefits the performance. Concretely, we quantitatively demonstrate the two benefits of domain knowledge in informed learning - regularizing the label-based supervision and supplementing the labeled samples - and reveal the trade-off between label and knowledge imperfectness in the bound of the population risk. Based on the theoretical analysis, we propose a generalized informed training objective to better exploit the benefits of knowledge and balance the label and knowledge imperfectness, which is validated by the population risk bound. Our analysis on sampling complexity sheds lights on how to choose the hyper-parameters for informed learning, and further justifies the advantages of knowledge informed learning., Comment: Accepted by ICML'22

We study online convex optimization with switching costs, a practically important but also extremely challenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers, ML-augmented online algorithms (also referred to as expert calibration in this paper) have been emerging as state of the art, with provable worst-case performance guarantees. Nonetheless, by using the standard practice of training an ML model as a standalone optimizer and plugging it into an ML-augmented algorithm, the average cost performance can be highly unsatisfactory. In order to address the "how to learn" challenge, we propose EC-L2O (expert-calibrated learning to optimize), which trains an ML-based optimizer by explicitly taking into account the downstream expert calibrator. To accomplish this, we propose a new differentiable expert calibrator that generalizes regularized online balanced descent and offers a provably better competitive ratio than pure ML predictions when the prediction error is large. For training, our loss function is a weighted sum of two different losses -- one minimizing the average ML prediction error for better robustness, and the other one minimizing the post-calibration average cost. We also provide theoretical analysis for EC-L2O, highlighting that expert calibration can be even beneficial for the average cost performance and that the high-percentile tail ratio of the cost achieved by EC-L2O to that of the offline optimal oracle (i.e., tail cost ratio) can be bounded. Finally, we test EC-L2O by running simulations for sustainable datacenter demand response. Our results demonstrate that EC-L2O can empirically achieve a lower average cost as well as a lower competitive ratio than the existing baseline algorithms., Comment: Pengfei Li and Jianyi Yang contributed equally. This paper has been accepted by and will be presented at the ACM SIGMETRICS/IFIP Performance 2022

In view of the performance limitations of fully-decoupled designs for neural architectures and accelerators, hardware-software co-design has been emerging to fully reap the benefits of flexible design spaces and optimize neural network performance. Nonetheless, such co-design also enlarges the total search space to practically infinity and presents substantial challenges. While the prior studies have been focusing on improving the search efficiency (e.g., via reinforcement learning), they commonly rely on co-searches over the entire architecture-accelerator design space. In this paper, we propose a \emph{semi}-decoupled approach to reduce the size of the total design space by orders of magnitude, yet without losing optimality. We first perform neural architecture search to obtain a small set of optimal architectures for one accelerator candidate. Importantly, this is also the set of (close-to-)optimal architectures for other accelerator designs based on the property that neural architectures' ranking orders in terms of inference latency and energy consumption on different accelerator designs are highly similar. Then, instead of considering all the possible architectures, we optimize the accelerator design only in combination with this small set of architectures, thus significantly reducing the total search cost. We validate our approach by conducting experiments on various architecture spaces for accelerator designs with different dataflows. Our results highlight that we can obtain the optimal design by only navigating over the reduced search space. The source code of this work is at \url{https://github.com/Ren-Research/CoDesign}., Comment: Accepted by and presented at the TinyML Research Symposium 2022

Hyperdimensional Computing (HDC) is facing infringement issues due to straightforward computations. This work, for the first time, raises a critical vulnerability of HDC, an attacker can reverse engineer the entire model, only requiring the unindexed hypervector memory. To mitigate this attack, we propose a defense strategy, namely HDLock, which significantly increases the reasoning cost of encoding. Specifically, HDLock adds extra feature hypervector combination and permutation in the encoding module. Compared to the standard HDC model, a two-layer-key HDLock can increase the adversarial reasoning complexity by 10 order of magnitudes without inference accuracy loss, with only 21% latency overhead., Comment: 7 pages, 9 figures, accepted by and to be presented at DAC 2022

Thanks to the tiny storage and efficient execution, hyperdimensional Computing (HDC) is emerging as a lightweight learning framework on resource-constrained hardware. Nonetheless, the existing HDC training relies on various heuristic methods, significantly limiting their inference accuracy. In this paper, we propose a new HDC framework, called LeHDC, which leverages a principled learning approach to improve the model accuracy. Concretely, LeHDC maps the existing HDC framework into an equivalent Binary Neural Network architecture, and employs a corresponding training strategy to minimize the training loss. Experimental validation shows that LeHDC outperforms previous HDC training strategies and can improve on average the inference accuracy over 15% compared to the baseline HDC., Comment: 7 pages, 6 figures, accepted by and to be presented at DAC 2022

By mimicking brain-like cognition and exploiting parallelism, hyperdimensional computing (HDC) classifiers have been emerging as a lightweight framework to achieve efficient on-device inference. Nonetheless, they have two fundamental drawbacks, heuristic training process and ultra-high dimension, which result in sub-optimal inference accuracy and large model sizes beyond the capability of tiny devices with stringent resource constraints. In this paper, we address these fundamental drawbacks and propose a low-dimensional computing (LDC) alternative. Specifically, by mapping our LDC classifier into an equivalent neural network, we optimize our model using a principled training approach. Most importantly, we can improve the inference accuracy while successfully reducing the ultra-high dimension of existing HDC models by orders of magnitude (e.g., 8000 vs. 4/64). We run experiments to evaluate our LDC classifier by considering different datasets for inference on tiny devices, and also implement different models on an FPGA platform for acceleration. The results highlight that our LDC classifier offers an overwhelming advantage over the existing brain-inspired HDC models and is particularly suitable for inference on tiny devices., Comment: 8 pages, 9 figures, accepted by and presented as a full paper at TinyML Research Symposium 2022

Learning to optimize (L2O) has recently emerged as a promising approach to solving optimization problems by exploiting the strong prediction power of neural networks and offering lower runtime complexity than conventional solvers. While L2O has been applied to various problems, a crucial yet challenging class of problems -- robust combinatorial optimization in the form of minimax optimization -- have largely remained under-explored. In addition to the exponentially large decision space, a key challenge for robust combinatorial optimization lies in the inner optimization problem, which is typically non-convex and entangled with outer optimization. In this paper, we study robust combinatorial optimization and propose a novel learning-based optimizer, called LRCO (Learning for Robust Combinatorial Optimization), which quickly outputs a robust solution in the presence of uncertain context. LRCO leverages a pair of learning-based optimizers -- one for the minimizer and the other for the maximizer -- that use their respective objective functions as losses and can be trained without the need of labels for training problem instances. To evaluate the performance of LRCO, we perform simulations for the task offloading problem in vehicular edge computing. Our results highlight that LRCO can greatly reduce the worst-case cost and improve robustness, while having a very low runtime complexity., Comment: Accepted by the IEEE International Conference on Computer Communications (INFOCOM) 2022

The rapid uptake of intelligent applications is pushing deep learning (DL) capabilities to Internet-of-Things (IoT). Despite the emergence of new tools for embedding deep neural networks (DNNs) into IoT devices, providing satisfactory Quality of Experience (QoE) to users is still challenging due to the heterogeneity in DNN architectures, IoT devices, and user preferences. This paper studies automated customization for DL inference on IoT devices (termed as on-thing inference), and our goal is to enhance user QoE by configuring the on-thing inference with an appropriate DNN for users under different usage scenarios. The core of our method is a DNN selection module that learns user QoE patterns on-the-fly and identifies the best-fit DNN for on-thing inference with the learned knowledge. It leverages a novel online learning algorithm, NeuralUCB, that has excellent generalization ability for handling various user QoE patterns. We also embed the knowledge transfer technique in NeuralUCB to expedite the learning process. However, NeuralUCB frequently solicits QoE ratings from users, which incurs non-negligible inconvenience. To address this problem, we design feedback solicitation schemes to reduce the number of QoE solicitations while maintaining the learning efficiency of NeuralUCB. A pragmatic problem, aggregated QoE, is further investigated to improve the practicality of our framework. We conduct experiments on both synthetic and real-world data. The results indicate that our method efficiently learns the user QoE pattern with few solicitations and provides drastic QoE enhancement for IoT devices.

Convolutional neural networks (CNNs) are used in numerous real-world applications such as vision-based autonomous driving and video content analysis. To run CNN inference on various target devices, hardware-aware neural architecture search (NAS) is crucial. A key requirement of efficient hardware-aware NAS is the fast evaluation of inference latencies in order to rank different architectures. While building a latency predictor for each target device has been commonly used in state of the art, this is a very time-consuming process, lacking scalability in the presence of extremely diverse devices. In this work, we address the scalability challenge by exploiting latency monotonicity -- the architecture latency rankings on different devices are often correlated. When strong latency monotonicity exists, we can re-use architectures searched for one proxy device on new target devices, without losing optimality. In the absence of strong latency monotonicity, we propose an efficient proxy adaptation technique to significantly boost the latency monotonicity. Finally, we validate our approach and conduct experiments with devices of different platforms on multiple mainstream search spaces, including MobileNet-V2, MobileNet-V3, NAS-Bench-201, ProxylessNAS and FBNet. Our results highlight that, by using just one proxy device, we can find almost the same Pareto-optimal architectures as the existing per-device NAS, while avoiding the prohibitive cost of building a latency predictor for each device. GitHub: https://github.com/Ren-Research/OneProxy, Comment: Accepted by the ACM SIGMETRICS 2022. Published in the Proceedings of the ACM on Measurement and Analysis of Computing Systems, vol. 5, no. 3, Article 34, December 2021. GitHub: https://github.com/Ren-Research/OneProxy

A standard assumption in contextual multi-arm bandit is that the true context is perfectly known before arm selection. Nonetheless, in many practical applications (e.g., cloud resource management), prior to arm selection, the context information can only be acquired by prediction subject to errors or adversarial modification. In this paper, we study a contextual bandit setting in which only imperfect context is available for arm selection while the true context is revealed at the end of each round. We propose two robust arm selection algorithms: MaxMinUCB (Maximize Minimum UCB) which maximizes the worst-case reward, and MinWD (Minimize Worst-case Degradation) which minimizes the worst-case regret. Importantly, we analyze the robustness of MaxMinUCB and MinWD by deriving both regret and reward bounds compared to an oracle that knows the true context. Our results show that as time goes on, MaxMinUCB and MinWD both perform as asymptotically well as their optimal counterparts that know the reward function. Finally, we apply MaxMinUCB and MinWD to online edge datacenter selection, and run synthetic simulations to validate our theoretical analysis.

We study a cooperative multi-agent multi-armed bandits with M agents and K arms. The goal of the agents is to minimized the cumulative regret. We adapt a traditional Thompson Sampling algoirthm under the distributed setting. However, with agent's ability to communicate, we note that communication may further reduce the upper bound of the regret for a distributed Thompson Sampling approach. To further improve the performance of distributed Thompson Sampling, we propose a distributed Elimination based Thompson Sampling algorithm that allow the agents to learn collaboratively. We analyse the algorithm under Bernoulli reward and derived a problem dependent upper bound on the cumulative regret., Comment: The paper is not finished and will not be updated

With the exploding popularity of machine learning, domain knowledge in various forms has been playing a crucial role in improving the learning performance, especially when training data is limited. Nonetheless, there is little understanding of to what extent domain knowledge can affect a machine learning task from a quantitative perspective. To increase the transparency and rigorously explain the role of domain knowledge in machine learning, we study the problem of quantifying the values of domain knowledge in terms of its contribution to the learning performance in the context of informed machine learning. We propose a quantification method based on Shapley value that fairly attributes the overall learning performance improvement to different domain knowledge. We also present Monte-Carlo sampling to approximate the fair value of domain knowledge with a polynomial time complexity. We run experiments of injecting symbolic domain knowledge into semi-supervised learning tasks on both MNIST and CIFAR10 datasets, providing quantitative values of different symbolic knowledge and rigorously explaining how it affects the machine learning performance in terms of test accuracy.

Deep neural networks (DNNs) have been increasingly deployed on and integrated with edge devices, such as mobile phones, drones, robots and wearables. To run DNN inference directly on edge devices (a.k.a. edge inference) with a satisfactory performance, optimizing the DNN design (e.g., network architecture and quantization policy) is crucial. While state-of-the-art DNN designs have leveraged performance predictors to speed up the optimization process, they are device-specific (i.e., each predictor for only one target device) and hence cannot scale well in the presence of extremely diverse edge devices. Moreover, even with performance predictors, the optimizer (e.g., search-based optimization) can still be time-consuming when optimizing DNNs for many different devices. In this work, we propose two approaches to scaling up DNN optimization. In the first approach, we reuse the performance predictors built on a proxy device, and leverage the performance monotonicity to scale up the DNN optimization without re-building performance predictors for each different device. In the second approach, we build scalable performance predictors that can estimate the resulting performance (e.g., inference accuracy/latency/energy) given a DNN-device pair, and use a neural network-based automated optimizer that takes both device features and optimization parameters as input and then directly outputs the optimal DNN design without going through a lengthy optimization process for each individual device., Comment: Position paper. New algorithm added. Part of the content (from Section 5 "Learning to Optimize") will be presented in the work-in-progress poster session of the ACM/IEEE Symposium on Edge Computing 2020

Inference accuracy of deep neural networks (DNNs) is a crucial performance metric, but can vary greatly in practice subject to actual test datasets and is typically unknown due to the lack of ground truth labels. This has raised significant concerns with trustworthiness of DNNs, especially in safety-critical applications. In this paper, we address trustworthiness of DNNs by using post-hoc processing to monitor the true inference accuracy on a user's dataset. Concretely, we propose a neural network-based accuracy monitor model, which only takes the deployed DNN's softmax probability output as its input and directly predicts if the DNN's prediction result is correct or not, thus leading to an estimate of the true inference accuracy. The accuracy monitor model can be pre-trained on a dataset relevant to the target application of interest, and only needs to actively label a small portion (1% in our experiments) of the user's dataset for model transfer. For estimation robustness, we further employ an ensemble of monitor models based on the Monte-Carlo dropout method. We evaluate our approach on different deployed DNN models for image classification and traffic sign detection over multiple datasets (including adversarial samples). The result shows that our accuracy monitor model provides a close-to-true accuracy estimation and outperforms the existing baseline methods., Comment: Accepted by the AISafety workshop co-located with IJCAI-PRICAI 2020

To increase the trustworthiness of deep neural network (DNN) classifiers, an accurate prediction confidence that represents the true likelihood of correctness is crucial. Towards this end, many post-hoc calibration methods have been proposed to leverage a lightweight model to map the target DNN's output layer into a calibrated confidence. Nonetheless, on an out-of-distribution (OOD) dataset in practice, the target DNN can often mis-classify samples with a high confidence, creating significant challenges for the existing calibration methods to produce an accurate confidence. In this paper, we propose a new post-hoc confidence calibration method, called CCAC (Confidence Calibration with an Auxiliary Class), for DNN classifiers on OOD datasets. The key novelty of CCAC is an auxiliary class in the calibration model which separates mis-classified samples from correctly classified ones, thus effectively mitigating the target DNN's being confidently wrong. We also propose a simplified version of CCAC to reduce free parameters and facilitate transfer to a new unseen dataset. Our experiments on different DNN models, datasets and applications show that CCAC can consistently outperform the prior post-hoc calibration methods.

Being an emerging class of in-memory computing architecture, brain-inspired hyperdimensional computing (HDC) mimics brain cognition and leverages random hypervectors (i.e., vectors with a dimensionality of thousands or even more) to represent features and to perform classification tasks. The unique hypervector representation enables HDC classifiers to exhibit high energy efficiency, low inference latency and strong robustness against hardware-induced bit errors. Consequently, they have been increasingly recognized as an appealing alternative to or even replacement of traditional deep neural networks (DNNs) for local on device classification, especially on low-power Internet of Things devices. Nonetheless, unlike their DNN counterparts, state-of-the-art designs for HDC classifiers are mostly security-oblivious, casting doubt on their safety and immunity to adversarial inputs. In this paper, we study for the first time adversarial attacks on HDC classifiers and highlight that HDC classifiers can be vulnerable to even minimally-perturbed adversarial samples. Concretely, using handwritten digit classification as an example, we construct a HDC classifier and formulate a grey-box attack problem, where an attacker's goal is to mislead the target HDC classifier to produce erroneous prediction labels while keeping the amount of added perturbation noise as little as possible. Then, we propose a modified genetic algorithm to generate adversarial samples within a reasonably small number of queries. Our results show that adversarial images generated by our algorithm can successfully mislead the HDC classifier to produce wrong prediction labels with a high probability (i.e., 78% when the HDC classifier uses a fixed majority rule for decision). Finally, we also present two defense strategies -- adversarial training and retraining-- to strengthen the security of HDC classifiers., Comment: 14 pages and 16 figures

Running deep neural network (DNN) inference on mobile devices, i.e., mobile inference, has become a growing trend, making inference less dependent on network connections and keeping private data locally. The prior studies on optimizing DNNs for mobile inference typically focus on the metric of average inference latency, thus implicitly assuming that mobile inference exhibits little latency variability. In this note, we conduct a preliminary measurement study on the latency variability of DNNs for mobile inference. We show that the inference latency variability can become quite significant in the presence of CPU resource contention. More interestingly, unlike the common belief that the relative performance superiority of DNNs on one device can carry over to another device and/or another level of resource contention, we highlight that a DNN model with a better latency performance than another model can become outperformed by the other model when resource contention be more severe or running on another device. Thus, when optimizing DNN models for mobile inference, only measuring the average latency may not be adequate; instead, latency variability under various conditions should be accounted for, including but not limited to different devices and different levels of CPU resource contention considered in this note.

Attacks based on power analysis have been long existing and studied, with some recent works focused on data exfiltration from victim systems without using conventional communications (e.g., WiFi). Nonetheless, prior works typically rely on intrusive direct power measurement, either by implanting meters in the power outlet or tapping into the power cable, thus jeopardizing the stealthiness of attacks. In this paper, we propose NoDE (Noise for Data Exfiltration), a new system for stealthy data exfiltration from enterprise desktop computers. Specifically, NoDE achieves data exfiltration over a building's power network by exploiting high-frequency voltage ripples (i.e., switching noises) generated by power factor correction circuits built into today's computers. Located at a distance and even from a different room, the receiver can non-intrusively measure the voltage of a power outlet to capture the high-frequency switching noises for online information decoding without supervised training/learning. To evaluate NoDE, we run experiments on seven different computers from top-vendors and using top brand power supply units. Our results show that for a single transmitter, NoDE achieves a rate of up to 28.48 bits/second with a distance of 90 feet (27.4 meters) without the line of sight, demonstrating a practically stealthy threat. Based on the orthogonality of switching noise frequencies of different computers, we also demonstrate simultaneous data exfiltration from four computers using only one receiver. Finally, we present a few possible defenses, such as installing noise filters, and discuss their limitations., Comment: 23 pages, 40 figures, to be presented at ACM SIGMETRICS, June 08~12, 2020, Boston, MA

Shared edge computing platforms deployed at the radio access network are expected to significantly improve quality of service delivered by Application Service Providers (ASPs) in a flexible and economic way. However, placing edge service in every possible edge site by an ASP is practically infeasible due to the ASP's prohibitive budget requirement. In this paper, we investigate the edge service placement problem of an ASP under a limited budget, where the ASP dynamically rents computing/storage resources in edge sites to host its applications in close proximity to end users. Since the benefit of placing edge service in a specific site is usually unknown to the ASP a priori, optimal placement decisions must be made while learning this benefit. We pose this problem as a novel combinatorial contextual bandit learning problem. It is "combinatorial" because only a limited number of edge sites can be rented to provide the edge service given the ASP's budget. It is "contextual" because we utilize user context information to enable finer-grained learning and decision making. To solve this problem and optimize the edge computing performance, we propose SEEN, a Spatial-temporal Edge sErvice placemeNt algorithm. Furthermore, SEEN is extended to scenarios with overlapping service coverage by incorporating a disjunctively constrained knapsack problem. In both cases, we prove that our algorithm achieves a sublinear regret bound when it is compared to an oracle algorithm that knows the exact benefit information. Simulations are carried out on a real-world dataset, whose results show that SEEN significantly outperforms benchmark solutions.

Mobile edge computing (a.k.a. fog computing) has recently emerged to enable in-situ processing of delay-sensitive applications at the edge of mobile networks. Providing grid power supply in support of mobile edge computing, however, is costly and even infeasible (in certain rugged or under-developed areas), thus mandating on-site renewable energy as a major or even sole power supply in increasingly many scenarios. Nonetheless, the high intermittency and unpredictability of renewable energy make it very challenging to deliver a high quality of service to users in energy harvesting mobile edge computing systems. In this paper, we address the challenge of incorporating renewables into mobile edge computing and propose an efficient reinforcement learning-based resource management algorithm, which learns on-the-fly the optimal policy of dynamic workload offloading (to the centralized cloud) and edge server provisioning to minimize the long-term system cost (including both service delay and operational cost). Our online learning algorithm uses a decomposition of the (offline) value iteration and (online) reinforcement learning, thus achieving a significant improvement of learning rate and run-time performance when compared to standard reinforcement learning algorithms such as Q-learning. We prove the convergence of the proposed algorithm and analytically show that the learned policy has a simple monotone structure amenable to practical implementation. Our simulation results validate the efficacy of our algorithm, which significantly improves the edge computing performance compared to fixed or myopic optimization schemes and conventional reinforcement learning algorithms., Comment: arXiv admin note: text overlap with arXiv:1701.01090 by other authors

Mobile edge computing (a.k.a. fog computing) has recently emerged to enable \emph{in-situ} processing of delay-sensitive applications at the edge of mobile networks. Providing grid power supply in support of mobile edge computing, however, is costly and even infeasible (in certain rugged or under-developed areas), thus mandating on-site renewable energy as a major or even sole power supply in increasingly many scenarios. Nonetheless, the high intermittency and unpredictability of renewable energy make it very challenging to deliver a high quality of service to users in renewable-powered mobile edge computing systems. In this paper, we address the challenge of incorporating renewables into mobile edge computing and propose an efficient reinforcement learning-based resource management algorithm, which learns on-the-fly the optimal policy of dynamic workload offloading (to centralized cloud) and edge server provisioning to minimize the long-term system cost (including both service delay and operational cost). Our online learning algorithm uses a decomposition of the (offline) value iteration and (online) reinforcement learning, thus achieving a significant improvement of learning rate and run-time performance when compared to standard reinforcement learning algorithms such as Q-learning., Comment: IEEE Globecom 2016

Participating in demand response programs is a promising tool for reducing energy costs in data centers by modulating energy consumption. Towards this end, data centers can employ a rich set of resource management knobs, such as workload shifting and dynamic server provisioning. Nonetheless, these knobs may not be readily available in a cloud data center (CDC) that serves cloud tenants/users, because workloads in CDCs are managed by tenants themselves who are typically charged based on a usage-based or flat-rate pricing and often have no incentive to cooperate with the CDC operator for demand response and cost saving. Towards breaking such "split incentive" hurdle, a few recent studies have tried market-based mechanisms, such as dynamic pricing, inside CDCs. However, such mechanisms often rely on complex designs that are hard to implement and difficult to cope with by tenants. To address this limitation, we propose a novel incentive mechanism that is not dynamic, i.e., it keeps pricing for cloud resources unchanged for a long period. While it charges tenants based on a Usage-based Pricing (UP) as used by today's major cloud operators, it rewards tenants proportionally based on the time length that tenants set as deadlines for completing their workloads. This new mechanism is called Usage-based Pricing with Monetary Reward (UPMR). We demonstrate the effectiveness of UPMR both analytically and empirically. We show that UPMR can reduce the CDC operator's energy cost by 12.9% while increasing its profit by 4.9%, compared to the state-of-the-art approaches used by today's CDC operators to charge their tenants.