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Conservative Contextual Bandits (CCBs) address safety in sequential decision making by requiring that an agent's policy, along with minimizing regret, also satisfies a safety constraint: the performance is not worse than a baseline policy (e.g., the policy that the company has in production) by more than $(1+\alpha)$ factor. Prior work developed UCB-style algorithms in the multi-armed [Wu et al., 2016] and contextual linear [Kazerouni et al., 2017] settings. However, in practice the cost of the arms is often a non-linear function, and therefore existing UCB algorithms are ineffective in such settings. In this paper, we consider CCBs beyond the linear case and develop two algorithms $\mathtt{C-SquareCB}$ and $\mathtt{C-FastCB}$, using Inverse Gap Weighting (IGW) based exploration and an online regression oracle. We show that the safety constraint is satisfied with high probability and that the regret of $\mathtt{C-SquareCB}$ is sub-linear in horizon $T$, while the regret of $\mathtt{C-FastCB}$ is first-order and is sub-linear in $L^*$, the cumulative loss of the optimal policy. Subsequently, we use a neural network for function approximation and online gradient descent as the regression oracle to provide $\tilde{O}(\sqrt{KT} + K/\alpha) $ and $\tilde{O}(\sqrt{KL^*} + K (1 + 1/\alpha))$ regret bounds, respectively. Finally, we demonstrate the efficacy of our algorithms on real-world data and show that they significantly outperform the existing baseline while maintaining the performance guarantee.

In Markov decision processes (MDPs), quantile risk measures such as Value-at-Risk are a standard metric for modeling RL agents' preferences for certain outcomes. This paper proposes a new Q-learning algorithm for quantile optimization in MDPs with strong convergence and performance guarantees. The algorithm leverages a new, simple dynamic program (DP) decomposition for quantile MDPs. Compared with prior work, our DP decomposition requires neither known transition probabilities nor solving complex saddle point equations and serves as a suitable foundation for other model-free RL algorithms. Our numerical results in tabular domains show that our Q-learning algorithm converges to its DP variant and outperforms earlier algorithms.

Fine-tuning text-to-image models with reward functions trained on human feedback data has proven effective for aligning model behavior with human intent. However, excessive optimization with such reward models, which serve as mere proxy objectives, can compromise the performance of fine-tuned models, a phenomenon known as reward overoptimization. To investigate this issue in depth, we introduce the Text-Image Alignment Assessment (TIA2) benchmark, which comprises a diverse collection of text prompts, images, and human annotations. Our evaluation of several state-of-the-art reward models on this benchmark reveals their frequent misalignment with human assessment. We empirically demonstrate that overoptimization occurs notably when a poorly aligned reward model is used as the fine-tuning objective. To address this, we propose TextNorm, a simple method that enhances alignment based on a measure of reward model confidence estimated across a set of semantically contrastive text prompts. We demonstrate that incorporating the confidence-calibrated rewards in fine-tuning effectively reduces overoptimization, resulting in twice as many wins in human evaluation for text-image alignment compared against the baseline reward models., Comment: ICLR 2024

The goal of an offline reinforcement learning (RL) algorithm is to learn optimal polices using historical (offline) data, without access to the environment for online exploration. One of the main challenges in offline RL is the distribution shift which refers to the difference between the state-action visitation distribution of the data generating policy and the learning policy. Many recent works have used the idea of pessimism for developing offline RL algorithms and characterizing their sample complexity under a relatively weak assumption of single policy concentrability. Different from the offline RL literature, the area of distributionally robust learning (DRL) offers a principled framework that uses a minimax formulation to tackle model mismatch between training and testing environments. In this work, we aim to bridge these two areas by showing that the DRL approach can be used to tackle the distributional shift problem in offline RL. In particular, we propose two offline RL algorithms using the DRL framework, for the tabular and linear function approximation settings, and characterize their sample complexity under the single policy concentrability assumption. We also demonstrate the superior performance our proposed algorithm through simulation experiments., Comment: 33 pages, preprint

Preference elicitation plays a central role in interactive recommender systems. Most preference elicitation approaches use either item queries that ask users to select preferred items from a slate, or attribute queries that ask them to express their preferences for item characteristics. Unfortunately, users often wish to describe their preferences using soft attributes for which no ground-truth semantics is given. Leveraging concept activation vectors for soft attribute semantics, we develop novel preference elicitation methods that can accommodate soft attributes and bring together both item and attribute-based preference elicitation. Our techniques query users using both items and soft attributes to update the recommender system's belief about their preferences to improve recommendation quality. We demonstrate the effectiveness of our methods vis-a-vis competing approaches on both synthetic and real-world datasets.

Recommender systems (RSs) play a central role in connecting users to content, products, and services, matching candidate items to users based on their preferences. While traditional RSs rely on implicit user feedback signals, conversational RSs interact with users in natural language. In this work, we develop a comPelling, Precise, Personalized, Preference-relevant language model (P4LM) that recommends items to users while putting emphasis on explaining item characteristics and their relevance. P4LM uses the embedding space representation of a user's preferences to generate compelling responses that are factually-grounded and relevant w.r.t. the user's preferences. Moreover, we develop a joint reward function that measures precision, appeal, and personalization, which we use as AI-based feedback in a reinforcement learning-based language model framework. Using the MovieLens 25M dataset, we demonstrate that P4LM delivers compelling, personalized movie narratives to users.

We study how to make decisions that minimize Bayesian regret in offline linear bandits. Prior work suggests that one must take actions with maximum lower confidence bound (LCB) on their reward. We argue that the reliance on LCB is inherently flawed in this setting and propose a new algorithm that directly minimizes upper bounds on the Bayesian regret using efficient conic optimization solvers. Our bounds build heavily on new connections to monetary risk measures. Proving a matching lower bound, we show that our upper bounds are tight, and by minimizing them we are guaranteed to outperform the LCB approach. Our numerical results on synthetic domains confirm that our approach is superior to LCB.

Learning from human feedback has been shown to improve text-to-image models. These techniques first learn a reward function that captures what humans care about in the task and then improve the models based on the learned reward function. Even though relatively simple approaches (e.g., rejection sampling based on reward scores) have been investigated, fine-tuning text-to-image models with the reward function remains challenging. In this work, we propose using online reinforcement learning (RL) to fine-tune text-to-image models. We focus on diffusion models, defining the fine-tuning task as an RL problem, and updating the pre-trained text-to-image diffusion models using policy gradient to maximize the feedback-trained reward. Our approach, coined DPOK, integrates policy optimization with KL regularization. We conduct an analysis of KL regularization for both RL fine-tuning and supervised fine-tuning. In our experiments, we show that DPOK is generally superior to supervised fine-tuning with respect to both image-text alignment and image quality. Our code is available at https://github.com/google-research/google-research/tree/master/dpok., Comment: NeurIPS 2023

Modern statistical estimation is often performed in a distributed setting where each sample belongs to a single user who shares their data with a central server. Users are typically concerned with preserving the privacy of their samples, and also with minimizing the amount of data they must transmit to the server. We give improved private and communication-efficient algorithms for estimating several popular measures of the entropy of a distribution. All of our algorithms have constant communication cost and satisfy local differential privacy. For a joint distribution over many variables whose conditional independence is given by a tree, we describe algorithms for estimating Shannon entropy that require a number of samples that is linear in the number of variables, compared to the quadratic sample complexity of prior work. We also describe an algorithm for estimating Gini entropy whose sample complexity has no dependence on the support size of the distribution and can be implemented using a single round of concurrent communication between the users and the server. In contrast, the previously best-known algorithm has high communication cost and requires the server to facilitate interaction between the users. Finally, we describe an algorithm for estimating collision entropy that generalizes the best known algorithm to the private and communication-efficient setting., Comment: Originally published at the 36th Conference on Neural Information Processing Systems (NeurIPS 2022). This version corrects some errors in the original version

Optimizing static risk-averse objectives in Markov decision processes is difficult because they do not admit standard dynamic programming equations common in Reinforcement Learning (RL) algorithms. Dynamic programming decompositions that augment the state space with discrete risk levels have recently gained popularity in the RL community. Prior work has shown that these decompositions are optimal when the risk level is discretized sufficiently. However, we show that these popular decompositions for Conditional-Value-at-Risk (CVaR) and Entropic-Value-at-Risk (EVaR) are inherently suboptimal regardless of the discretization level. In particular, we show that a saddle point property assumed to hold in prior literature may be violated. However, a decomposition does hold for Value-at-Risk and our proof demonstrates how this risk measure differs from CVaR and EVaR. Our findings are significant because risk-averse algorithms are used in high-stake environments, making their correctness much more critical.

Video captioning (VC) is a fast-moving, cross-disciplinary area of research that bridges work in the fields of computer vision, natural language processing (NLP), linguistics, and human-computer interaction. In essence, VC involves understanding a video and describing it with language. Captioning is used in a host of applications from creating more accessible interfaces (e.g., low-vision navigation) to video question answering (V-QA), video retrieval and content generation. This survey covers deep learning-based VC, including but, not limited to, attention-based architectures, graph networks, reinforcement learning, adversarial networks, dense video captioning (DVC), and more. We discuss the datasets and evaluation metrics used in the field, and limitations, applications, challenges, and future directions for VC., Comment: 42 pages, 10 figures

Deep generative models have shown impressive results in text-to-image synthesis. However, current text-to-image models often generate images that are inadequately aligned with text prompts. We propose a fine-tuning method for aligning such models using human feedback, comprising three stages. First, we collect human feedback assessing model output alignment from a set of diverse text prompts. We then use the human-labeled image-text dataset to train a reward function that predicts human feedback. Lastly, the text-to-image model is fine-tuned by maximizing reward-weighted likelihood to improve image-text alignment. Our method generates objects with specified colors, counts and backgrounds more accurately than the pre-trained model. We also analyze several design choices and find that careful investigations on such design choices are important in balancing the alignment-fidelity tradeoffs. Our results demonstrate the potential for learning from human feedback to significantly improve text-to-image models.

Reinforcement learning (RL) has shown great promise for developing dialogue management (DM) agents that are non-myopic, conduct rich conversations, and maximize overall user satisfaction. Despite recent developments in RL and language models (LMs), using RL to power conversational chatbots remains challenging, in part because RL requires online exploration to learn effectively, whereas collecting novel human-bot interactions can be expensive and unsafe. This issue is exacerbated by the combinatorial action spaces facing these algorithms, as most LM agents generate responses at the word level. We develop a variety of RL algorithms, specialized to dialogue planning, that leverage recent Mixture-of-Expert Language Models (MoE-LMs) -- models that capture diverse semantics, generate utterances reflecting different intents, and are amenable for multi-turn DM. By exploiting MoE-LM structure, our methods significantly reduce the size of the action space and improve the efficacy of RL-based DM. We evaluate our methods in open-domain dialogue to demonstrate their effectiveness w.r.t.\ the diversity of intent in generated utterances and overall DM performance., Comment: Thirty-seventh Conference on Neural Information Processing Systems (NeurIPS 2023)

Many practical applications, such as recommender systems and learning to rank, involve solving multiple similar tasks. One example is learning of recommendation policies for users with similar movie preferences, where the users may still rank the individual movies slightly differently. Such tasks can be organized in a hierarchy, where similar tasks are related through a shared structure. In this work, we formulate this problem as a contextual off-policy optimization in a hierarchical graphical model from logged bandit feedback. To solve the problem, we propose a hierarchical off-policy optimization algorithm (HierOPO), which estimates the parameters of the hierarchical model and then acts pessimistically with respect to them. We instantiate HierOPO in linear Gaussian models, for which we also provide an efficient implementation and analysis. We prove per-task bounds on the suboptimality of the learned policies, which show a clear improvement over not using the hierarchical model. We also evaluate the policies empirically. Our theoretical and empirical results show a clear advantage of using the hierarchy over solving each task independently., Comment: 14 pages, 3 figures

We introduce new planning and reinforcement learning algorithms for discounted MDPs that utilize an approximate model of the environment to accelerate the convergence of the value function. Inspired by the splitting approach in numerical linear algebra, we introduce Operator Splitting Value Iteration (OS-VI) for both Policy Evaluation and Control problems. OS-VI achieves a much faster convergence rate when the model is accurate enough. We also introduce a sample-based version of the algorithm called OS-Dyna. Unlike the traditional Dyna architecture, OS-Dyna still converges to the correct value function in presence of model approximation error., Comment: Accepted to NeurIPS2022

Prior work on safe Reinforcement Learning (RL) has studied risk-aversion to randomness in dynamics (aleatory) and to model uncertainty (epistemic) in isolation. We propose and analyze a new framework to jointly model the risk associated with epistemic and aleatory uncertainties in finite-horizon and discounted infinite-horizon MDPs. We call this framework that combines Risk-Averse and Soft-Robust methods RASR. We show that when the risk-aversion is defined using either EVaR or the entropic risk, the optimal policy in RASR can be computed efficiently using a new dynamic program formulation with a time-dependent risk level. As a result, the optimal risk-averse policies are deterministic but time-dependent, even in the infinite-horizon discounted setting. We also show that particular RASR objectives reduce to risk-averse RL with mean posterior transition probabilities. Our empirical results show that our new algorithms consistently mitigate uncertainty as measured by EVaR and other standard risk measures.

The goal of robust reinforcement learning (RL) is to learn a policy that is robust against the uncertainty in model parameters. Parameter uncertainty commonly occurs in many real-world RL applications due to simulator modeling errors, changes in the real-world system dynamics over time, and adversarial disturbances. Robust RL is typically formulated as a max-min problem, where the objective is to learn the policy that maximizes the value against the worst possible models that lie in an uncertainty set. In this work, we propose a robust RL algorithm called Robust Fitted Q-Iteration (RFQI), which uses only an offline dataset to learn the optimal robust policy. Robust RL with offline data is significantly more challenging than its non-robust counterpart because of the minimization over all models present in the robust Bellman operator. This poses challenges in offline data collection, optimization over the models, and unbiased estimation. In this work, we propose a systematic approach to overcome these challenges, resulting in our RFQI algorithm. We prove that RFQI learns a near-optimal robust policy under standard assumptions and demonstrate its superior performance on standard benchmark problems., Comment: Appeared in Neural Information Processing Systems (NeurIPS) 2022

Learning task-oriented dialog policies via reinforcement learning typically requires large amounts of interaction with users, which in practice renders such methods unusable for real-world applications. In order to reduce the data requirements, we propose to leverage data from across different dialog domains, thereby reducing the amount of data required from each given domain. In particular, we propose to learn domain-agnostic action embeddings, which capture general-purpose structure that informs the system how to act given the current dialog context, and are then specialized to a specific domain. We show how this approach is capable of learning with significantly less interaction with users, with a reduction of 35% in the number of dialogs required to learn, and to a higher level of proficiency than training separate policies for each domain on a set of simulated domains., Comment: Presented in the Conversational AI Workshop, NeurIPS 2019

Despite recent advancements in language models (LMs), their application to dialogue management (DM) problems and ability to carry on rich conversations remain a challenge. We use reinforcement learning (RL) to develop a dialogue agent that avoids being short-sighted (outputting generic utterances) and maximizes overall user satisfaction. Most existing RL approaches to DM train the agent at the word-level, and thus, have to deal with a combinatorially complex action space even for a medium-size vocabulary. As a result, they struggle to produce a successful and engaging dialogue even if they are warm-started with a pre-trained LM. To address this issue, we develop a RL-based DM using a novel mixture of expert language model (MoE-LM) that consists of (i) a LM capable of learning diverse semantics for conversation histories, (ii) a number of {\em specialized} LMs (or experts) capable of generating utterances corresponding to a particular attribute or personality, and (iii) a RL-based DM that performs dialogue planning with the utterances generated by the experts. Our MoE approach provides greater flexibility to generate sensible utterances with different intents and allows RL to focus on conversational-level DM. We compare it with SOTA baselines on open-domain dialogues and demonstrate its effectiveness both in terms of the diversity and sensibility of the generated utterances and the overall DM performance.

We study a collaborative multi-agent stochastic linear bandit setting, where $N$ agents that form a network communicate locally to minimize their overall regret. In this setting, each agent has its own linear bandit problem (its own reward parameter) and the goal is to select the best global action w.r.t. the average of their reward parameters. At each round, each agent proposes an action, and one action is randomly selected and played as the network action. All the agents observe the corresponding rewards of the played actions and use an accelerated consensus procedure to compute an estimate of the average of the rewards obtained by all the agents. We propose a distributed upper confidence bound (UCB) algorithm and prove a high probability bound on its $T$-round regret in which we include a linear growth of regret associated with each communication round. Our regret bound is of order $\mathcal{O}\Big(\sqrt{\frac{T}{N \log(1/|\lambda_2|)}}\cdot (\log T)^2\Big)$, where $\lambda_2$ is the second largest (in absolute value) eigenvalue of the communication matrix.

In this work we investigate meta-learning (or learning-to-learn) approaches in multi-task linear stochastic bandit problems that can originate from multiple environments. Inspired by the work of [1] on meta-learning in a sequence of linear bandit problems whose parameters are sampled from a single distribution (i.e., a single environment), here we consider the feasibility of meta-learning when task parameters are drawn from a mixture distribution instead. For this problem, we propose a regularized version of the OFUL algorithm that, when trained on tasks with labeled environments, achieves low regret on a new task without requiring knowledge of the environment from which the new task originates. Specifically, our regret bound for the new algorithm captures the effect of environment misclassification and highlights the benefits over learning each task separately or meta-learning without recognition of the distinct mixture components.

In risk-averse reinforcement learning (RL), the goal is to optimize some risk measure of the returns. A risk measure often focuses on the worst returns out of the agent's experience. As a result, standard methods for risk-averse RL often ignore high-return strategies. We prove that under certain conditions this inevitably leads to a local-optimum barrier, and propose a soft risk mechanism to bypass it. We also devise a novel Cross Entropy module for risk sampling, which (1) preserves risk aversion despite the soft risk; (2) independently improves sample efficiency. By separating the risk aversion of the sampler and the optimizer, we can sample episodes with poor conditions, yet optimize with respect to successful strategies. We combine these two concepts in CeSoR - Cross-entropy Soft-Risk optimization algorithm - which can be applied on top of any risk-averse policy gradient (PG) method. We demonstrate improved risk aversion in maze navigation, autonomous driving, and resource allocation benchmarks, including in scenarios where standard risk-averse PG completely fails., Comment: Accepted to NeurIPS 2022

We study a sequential decision problem where the learner faces a sequence of $K$-armed bandit tasks. The task boundaries might be known (the bandit meta-learning setting), or unknown (the non-stationary bandit setting). For a given integer $M\le K$, the learner aims to compete with the best subset of arms of size $M$. We design an algorithm based on a reduction to bandit submodular maximization, and show that, for $T$ rounds comprised of $N$ tasks, in the regime of large number of tasks and small number of optimal arms $M$, its regret in both settings is smaller than the simple baseline of $\tilde{O}(\sqrt{KNT})$ that can be obtained by using standard algorithms designed for non-stationary bandit problems. For the bandit meta-learning problem with fixed task length $\tau$, we show that the regret of the algorithm is bounded as $\tilde{O}(NM\sqrt{M \tau}+N^{2/3}M\tau)$. Under additional assumptions on the identifiability of the optimal arms in each task, we show a bandit meta-learning algorithm with an improved $\tilde{O}(N\sqrt{M \tau}+N^{1/2}\sqrt{M K \tau})$ regret.

We develop a meta-learning framework for simple regret minimization in bandits. In this framework, a learning agent interacts with a sequence of bandit tasks, which are sampled i.i.d.\ from an unknown prior distribution, and learns its meta-parameters to perform better on future tasks. We propose the first Bayesian and frequentist meta-learning algorithms for this setting. The Bayesian algorithm has access to a prior distribution over the meta-parameters and its meta simple regret over $m$ bandit tasks with horizon $n$ is mere $\tilde{O}(m / \sqrt{n})$. On the other hand, the meta simple regret of the frequentist algorithm is $\tilde{O}(\sqrt{m} n + m/ \sqrt{n})$. While its regret is worse, the frequentist algorithm is more general because it does not need a prior distribution over the meta-parameters. It can also be analyzed in more settings. We instantiate our algorithms for several classes of bandit problems. Our algorithms are general and we complement our theory by evaluating them empirically in several environments.

Interactive recommender systems have emerged as a promising paradigm to overcome the limitations of the primitive user feedback used by traditional recommender systems (e.g., clicks, item consumption, ratings). They allow users to express intent, preferences, constraints, and contexts in a richer fashion, often using natural language (including faceted search and dialogue). Yet more research is needed to find the most effective ways to use this feedback. One challenge is inferring a user's semantic intent from the open-ended terms or attributes often used to describe a desired item, and using it to refine recommendation results. Leveraging concept activation vectors (CAVs) [26], a recently developed approach for model interpretability in machine learning, we develop a framework to learn a representation that captures the semantics of such attributes and connects them to user preferences and behaviors in recommender systems. One novel feature of our approach is its ability to distinguish objective and subjective attributes (both subjectivity of degree and of sense), and associate different senses of subjective attributes with different users. We demonstrate on both synthetic and real-world data sets that our CAV representation not only accurately interprets users' subjective semantics, but can also be used to improve recommendations through interactive item critiquing.

Mean rewards of actions are often correlated. The form of these correlations may be complex and unknown a priori, such as the preferences of a user for recommended products and their categories. To maximize statistical efficiency, it is important to leverage these correlations when learning. We formulate a bandit variant of this problem where the correlations of mean action rewards are represented by a hierarchical Bayesian model with latent variables. Since the hierarchy can have multiple layers, we call it deep. We propose a hierarchical Thompson sampling algorithm (HierTS) for this problem, and show how to implement it efficiently for Gaussian hierarchies. The efficient implementation is possible due to a novel exact hierarchical representation of the posterior, which itself is of independent interest. We use this exact posterior to analyze the Bayes regret of HierTS in Gaussian bandits. Our analysis reflects the structure of the problem, that the regret decreases with the prior width, and also shows that hierarchies reduce the regret by non-constant factors in the number of actions. We confirm these theoretical findings empirically, in both synthetic and real-world experiments.

Meta-, multi-task, and federated learning can be all viewed as solving similar tasks, drawn from a distribution that reflects task similarities. We provide a unified view of all these problems, as learning to act in a hierarchical Bayesian bandit. We propose and analyze a natural hierarchical Thompson sampling algorithm (HierTS) for this class of problems. Our regret bounds hold for many variants of the problems, including when the tasks are solved sequentially or in parallel; and show that the regret decreases with a more informative prior. Our proofs rely on a novel total variance decomposition that can be applied beyond our models. Our theory is complemented by experiments, which show that the hierarchy helps with knowledge sharing among the tasks. This confirms that hierarchical Bayesian bandits are a universal and statistically-efficient tool for learning to act with similar bandit tasks., Comment: Proceedings of the 25th International Conference on Artificial Intelligence and Statistics

We study Thompson sampling (TS) in online decision making, where the uncertain environment is sampled from a mixture distribution. This is relevant in multi-task learning, where a learning agent faces different classes of problems. We incorporate this structure in a natural way by initializing TS with a mixture prior, and call the resulting algorithm MixTS. To analyze MixTS, we develop a novel and general proof technique for analyzing the concentration of mixture distributions. We use it to prove Bayes regret bounds for MixTS in both linear bandits and finite-horizon reinforcement learning. Our bounds capture the structure of the prior, depend on the number of mixture components and their widths. We also demonstrate the empirical effectiveness of MixTS in synthetic and real-world experiments., Comment: Proceedings of the 25th International Conference on Artificial Intelligence and Statistics

We study two model selection settings in stochastic linear bandits (LB). In the first setting, which we refer to as feature selection, the expected reward of the LB problem is in the linear span of at least one of $M$ feature maps (models). In the second setting, the reward parameter of the LB problem is arbitrarily selected from $M$ models represented as (possibly) overlapping balls in $\mathbb R^d$. However, the agent only has access to misspecified models, i.e.,~estimates of the centers and radii of the balls. We refer to this setting as parameter selection. For each setting, we develop and analyze a computationally efficient algorithm that is based on a reduction from bandits to full-information problems. This allows us to obtain regret bounds that are not worse (up to a $\sqrt{\log M}$ factor) than the case where the true model is known. This is the best-reported dependence on the number of models $M$ in these settings. Finally, we empirically show the effectiveness of our algorithms using synthetic and real-world experiments.

Best-arm identification (BAI) in a fixed-budget setting is a bandit problem where the learning agent maximizes the probability of identifying the optimal (best) arm after a fixed number of observations. Most works on this topic study unstructured problems with a small number of arms, which limits their applicability. We propose a general tractable algorithm that incorporates the structure, by successively eliminating suboptimal arms based on their mean reward estimates from a joint generalization model. We analyze our algorithm in linear and generalized linear models (GLMs), and propose a practical implementation based on a G-optimal design. In linear models, our algorithm has competitive error guarantees to prior works and performs at least as well empirically. In GLMs, this is the first practical algorithm with analysis for fixed-budget BAI.

Machine learning models trained on uncurated datasets can often end up adversely affecting inputs belonging to underrepresented groups. To address this issue, we consider the problem of adaptively constructing training sets which allow us to learn classifiers that are fair in a minimax sense. We first propose an adaptive sampling algorithm based on the principle of optimism, and derive theoretical bounds on its performance. We also propose heuristic extensions of this algorithm suitable for application to large scale, practical problems. Next, by deriving algorithm independent lower-bounds for a specific class of problems, we show that the performance achieved by our adaptive scheme cannot be improved in general. We then validate the benefits of adaptively constructing training sets via experiments on synthetic tasks with logistic regression classifiers, as well as on several real-world tasks using convolutional neural networks (CNNs)., Comment: 30 pages, 13 figures

Users of recommender systems often behave in a non-stationary fashion, due to their evolving preferences and tastes over time. In this work, we propose a practical approach for fast personalization to non-stationary users. The key idea is to frame this problem as a latent bandit, where the prototypical models of user behavior are learned offline and the latent state of the user is inferred online from its interactions with the models. We call this problem a non-stationary latent bandit. We propose Thompson sampling algorithms for regret minimization in non-stationary latent bandits, analyze them, and evaluate them on a real-world dataset. The main strength of our approach is that it can be combined with rich offline-learned models, which can be misspecified, and are subsequently fine-tuned online using posterior sampling. In this way, we naturally combine the strengths of offline and online learning., Comment: 15 pages, 4 figures

In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately, such policies are typically overly conservative as the percentile criterion is non-convex, difficult to optimize, and ignores the mean performance. To overcome these shortcomings, we study the soft-robust criterion, which uses risk measures to balance the mean and percentile criterion better. In this paper, we establish the soft-robust criterion's fundamental properties, show that it is NP-hard to optimize, and propose and analyze two algorithms to approximately optimize it. Our theoretical analyses and empirical evaluations demonstrate that our algorithms compute much less conservative solutions than the existing approximate methods for optimizing the percentile-criterion.

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian approximation and ensemble learning techniques are two most widely-used UQ methods in the literature. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning. Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods. Finally, we briefly highlight the fundamental research challenges faced by UQ methods and discuss the future research directions in this field.

Off-policy policy optimization is a challenging problem in reinforcement learning (RL). The algorithms designed for this problem often suffer from high variance in their estimators, which results in poor sample efficiency, and have issues with convergence. A few variance-reduced on-policy policy gradient algorithms have been recently proposed that use methods from stochastic optimization to reduce the variance of the gradient estimate in the REINFORCE algorithm. However, these algorithms are not designed for the off-policy setting and are memory-inefficient, since they need to collect and store a large ``reference'' batch of samples from time to time. To achieve variance-reduced off-policy-stable policy optimization, we propose an algorithm family that is memory-efficient, stochastically variance-reduced, and capable of learning from off-policy samples. Empirical studies validate the effectiveness of the proposed approaches.

We study the problem of obtaining accurate policy gradient estimates using a finite number of samples. Monte-Carlo methods have been the default choice for policy gradient estimation, despite suffering from high variance in the gradient estimates. On the other hand, more sample efficient alternatives like Bayesian quadrature methods have received little attention due to their high computational complexity. In this work, we propose deep Bayesian quadrature policy gradient (DBQPG), a computationally efficient high-dimensional generalization of Bayesian quadrature, for policy gradient estimation. We show that DBQPG can substitute Monte-Carlo estimation in policy gradient methods, and demonstrate its effectiveness on a set of continuous control benchmarks. In comparison to Monte-Carlo estimation, DBQPG provides (i) more accurate gradient estimates with a significantly lower variance, (ii) a consistent improvement in the sample complexity and average return for several deep policy gradient algorithms, and, (iii) the uncertainty in gradient estimation that can be incorporated to further improve the performance., Comment: Conference paper: AAAI-21. Code available at https://github.com/Akella17/Deep-Bayesian-Quadrature-Policy-Optimization

A major challenge in modern reinforcement learning (RL) is efficient control of dynamical systems from high-dimensional sensory observations. Learning controllable embedding (LCE) is a promising approach that addresses this challenge by embedding the observations into a lower-dimensional latent space, estimating the latent dynamics, and utilizing it to perform control in the latent space. Two important questions in this area are how to learn a representation that is amenable to the control problem at hand, and how to achieve an end-to-end framework for representation learning and control. In this paper, we take a few steps towards addressing these questions. We first formulate a LCE model to learn representations that are suitable to be used by a policy iteration style algorithm in the latent space. We call this model control-aware representation learning (CARL). We derive a loss function for CARL that has close connection to the prediction, consistency, and curvature (PCC) principle for representation learning. We derive three implementations of CARL. In the offline implementation, we replace the locally-linear control algorithm (e.g.,~iLQR) used by the existing LCE methods with a RL algorithm, namely model-based soft actor-critic, and show that it results in significant improvement. In online CARL, we interleave representation learning and control, and demonstrate further gain in performance. Finally, we propose value-guided CARL, a variation in which we optimize a weighted version of the CARL loss function, where the weights depend on the TD-error of the current policy. We evaluate the proposed algorithms by extensive experiments on benchmark tasks and compare them with several LCE baselines.

We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies, whose expected cumulative reward over the course of $T$ rounds is maximum, and each has an expected cost below a certain threshold $\tau$. We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB), and prove an $\widetilde{\mathcal{O}}(\frac{d\sqrt{T}}{\tau-c_0})$ bound on its $T$-round regret, where the denominator is the difference between the constraint threshold and the cost of a known feasible action. We further specialize our results to multi-armed bandits and propose a computationally efficient algorithm for this setting. We prove a regret bound of $\widetilde{\mathcal{O}}(\frac{\sqrt{KT}}{\tau - c_0})$ for this algorithm in $K$-armed bandits, which is a $\sqrt{K}$ improvement over the regret bound we obtain by simply casting multi-armed bandits as an instance of contextual linear bandits and using the regret bound of OPLB. We also prove a lower-bound for the problem studied in the paper and provide simulations to validate our theoretical results., Comment: 9 pages

Model-based reinforcement learning (RL) algorithms allow us to combine model-generated data with those collected from interaction with the real system in order to alleviate the data efficiency problem in RL. However, designing such algorithms is often challenging because the bias in simulated data may overshadow the ease of data generation. A potential solution to this challenge is to jointly learn and improve model and policy using a universal objective function. In this paper, we leverage the connection between RL and probabilistic inference, and formulate such an objective function as a variational lower-bound of a log-likelihood. This allows us to use expectation maximization (EM) and iteratively fix a baseline policy and learn a variational distribution, consisting of a model and a policy (E-step), followed by improving the baseline policy given the learned variational distribution (M-step). We propose model-based and model-free policy iteration (actor-critic) style algorithms for the E-step and show how the variational distribution learned by them can be used to optimize the M-step in a fully model-based fashion. Our experiments on a number of continuous control tasks show that despite being more complex, our model-based (E-step) algorithm, called {\em variational model-based policy optimization} (VMBPO), is more sample-efficient and robust to hyper-parameter tuning than its model-free (E-step) counterpart. Using the same control tasks, we also compare VMBPO with several state-of-the-art model-based and model-free RL algorithms and show its sample efficiency and performance.

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function. We also conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and do not provide any finite-sample analysis. We also propose an accelerated algorithm, called GTD2-MP, that uses proximal ``mirror maps'' to yield an improved convergence rate. The results of our theoretical analysis imply that the GTD family of algorithms are comparable and may indeed be preferred over existing least squares TD methods for off-policy learning, due to their linear complexity. We provide experimental results showing the improved performance of our accelerated gradient TD methods., Comment: Journal of Artificial Intelligence (JAIR)

In this paper, we analyze the convergence rate of the gradient temporal difference learning (GTD) family of algorithms. Previous analyses of this class of algorithms use ODE techniques to prove asymptotic convergence, and to the best of our knowledge, no finite-sample analysis has been done. Moreover, there has been not much work on finite-sample analysis for convergent off-policy reinforcement learning algorithms. In this paper, we formulate GTD methods as stochastic gradient algorithms w.r.t.~a primal-dual saddle-point objective function, and then conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Two revised algorithms are also proposed, namely projected GTD2 and GTD2-MP, which offer improved convergence guarantees and acceleration, respectively. The results of our theoretical analysis show that the GTD family of algorithms are indeed comparable to the existing LSTD methods in off-policy learning scenarios., Comment: 31st Conference on Uncertainty in Artificial Intelligence (UAI). arXiv admin note: substantial text overlap with arXiv:2006.03976

Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion of safety to ensure that it does not harm either the agent or the environment. Stability is a crucial notion of safety, whose violation can certainly cause unsafe behaviors. Lyapunov functions are effective tools to assess stability in nonlinear dynamical systems. In this paper, we combine an improving Lyapunov function with automatic controller synthesis in an iterative fashion to obtain control policies with large safe regions. We propose a two-player collaborative algorithm that alternates between estimating a Lyapunov function and deriving a controller that gradually enlarges the stability region of the closed-loop system. We provide theoretical results on the class of systems that can be treated with the proposed algorithm and empirically evaluate the effectiveness of our method using an exemplary dynamical system., Comment: 27 pages

Mirror descent (MD), a well-known first-order method in constrained convex optimization, has recently been shown as an important tool to analyze trust-region algorithms in reinforcement learning (RL). However, there remains a considerable gap between such theoretically analyzed algorithms and the ones used in practice. Inspired by this, we propose an efficient RL algorithm, called {\em mirror descent policy optimization} (MDPO). MDPO iteratively updates the policy by {\em approximately} solving a trust-region problem, whose objective function consists of two terms: a linearization of the standard RL objective and a proximity term that restricts two consecutive policies to be close to each other. Each update performs this approximation by taking multiple gradient steps on this objective function. We derive {\em on-policy} and {\em off-policy} variants of MDPO, while emphasizing important design choices motivated by the existing theory of MD in RL. We highlight the connections between on-policy MDPO and two popular trust-region RL algorithms: TRPO and PPO, and show that explicitly enforcing the trust-region constraint is in fact {\em not} a necessity for high performance gains in TRPO. We then show how the popular soft actor-critic (SAC) algorithm can be derived by slight modifications of off-policy MDPO. Overall, MDPO is derived from the MD principles, offers a unified approach to viewing a number of popular RL algorithms, and performs better than or on-par with TRPO, PPO, and SAC in a number of continuous control tasks. Code is available at \url{https://github.com/manantomar/Mirror-Descent-Policy-Optimization}.

We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP). Efficient exploration in this problem requires the agent to identify the regions in which estimating the model is more difficult and then exploit this knowledge to collect more samples there. In this paper, we formalize this problem, introduce the first algorithm to learn an $\epsilon$-accurate estimate of the dynamics, and provide its sample complexity analysis. While this algorithm enjoys strong guarantees in the large-sample regime, it tends to have a poor performance in early stages of exploration. To address this issue, we propose an algorithm that is based on maximum weighted entropy, a heuristic that stems from common sense and our theoretical analysis. The main idea here is to cover the entire state-action space with the weight proportional to the noise in the transitions. Using a number of simple domains with heterogeneous noise in their transitions, we show that our heuristic-based algorithm outperforms both our original algorithm and the maximum entropy algorithm in the small sample regime, while achieving similar asymptotic performance as that of the original algorithm.

High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the observations into a lower dimensional latent space, estimating the latent dynamics, and then performing control directly in the latent space. To ensure the learned latent dynamics are predictive of next-observations, all existing LCE approaches decode back into the observation space and explicitly perform next-observation prediction---a challenging high-dimensional task that furthermore introduces a large number of nuisance parameters (i.e., the decoder) which are discarded during control. In this paper, we propose a novel information-theoretic LCE approach and show theoretically that explicit next-observation prediction can be replaced with predictive coding. We then use predictive coding to develop a decoder-free LCE model whose latent dynamics are amenable to locally-linear control. Extensive experiments on benchmark tasks show that our model reliably learns a controllable latent space that leads to superior performance when compared with state-of-the-art LCE baselines.

This paper considers the problem of learning a model in model-based reinforcement learning (MBRL). We examine how the planning module of an MBRL algorithm uses the model, and propose that the model learning module should incorporate the way the planner is going to use the model. This is in contrast to conventional model learning approaches, such as those based on maximum likelihood estimate, that learn a predictive model of the environment without explicitly considering the interaction of the model and the planner. We focus on policy gradient type of planning algorithms and derive new loss functions for model learning that incorporate how the planner uses the model. We call this approach Policy-Aware Model Learning (PAML). We theoretically analyze a generic model-based policy gradient algorithm and provide a convergence guarantee for the optimized policy. We also empirically evaluate PAML on some benchmark problems, showing promising results.

In many fields such as digital marketing, healthcare, finance, and robotics, it is common to have a well-tested and reliable baseline policy running in production (e.g., a recommender system). Nonetheless, the baseline policy is often suboptimal. In this case, it is desirable to deploy online learning algorithms (e.g., a multi-armed bandit algorithm) that interact with the system to learn a better/optimal policy under the constraint that during the learning process the performance is almost never worse than the performance of the baseline itself. In this paper, we study the conservative learning problem in the contextual linear bandit setting and introduce a novel algorithm, the Conservative Constrained LinUCB (CLUCB2). We derive regret bounds for CLUCB2 that match existing results and empirically show that it outperforms state-of-the-art conservative bandit algorithms in a number of synthetic and real-world problems. Finally, we consider a more realistic constraint where the performance is verified only at predefined checkpoints (instead of at every step) and show how this relaxed constraint favorably impacts the regret and empirical performance of CLUCB2.

While learning in an unknown Markov Decision Process (MDP), an agent should trade off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward. Although the agent will eventually learn a good or optimal policy, there is no guarantee on the quality of the intermediate policies. This lack of control is undesired in real-world applications where a minimum requirement is that the executed policies are guaranteed to perform at least as well as an existing baseline. In this paper, we introduce the notion of conservative exploration for average reward and finite horizon problems. We present two optimistic algorithms that guarantee (w.h.p.) that the conservative constraint is never violated during learning. We derive regret bounds showing that being conservative does not hinder the learning ability of these algorithms., Comment: AISTATS 2020

We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To present a unified treatment of these distances, we first propose a general optimistic tracking algorithm and analyze its sample allocation performance w.r.t.~an oracle. We then instantiate this algorithm for the four distance measures and derive bounds on the regret of their resulting allocation schemes. We verify our theoretical findings through some experiments. Finally, we show that the techniques developed in the paper can be easily extended to the related setting of minimizing the average error (in terms of the four distances) in learning a set of distributions., Comment: 40 pages, 3 figures

Multi-step greedy policies have been extensively used in model-based reinforcement learning (RL), both when a model of the environment is available (e.g.,~in the game of Go) and when it is learned. In this paper, we explore their benefits in model-free RL, when employed using multi-step dynamic programming algorithms: $\kappa$-Policy Iteration ($\kappa$-PI) and $\kappa$-Value Iteration ($\kappa$-VI). These methods iteratively compute the next policy ($\kappa$-PI) and value function ($\kappa$-VI) by solving a surrogate decision problem with a shaped reward and a smaller discount factor. We derive model-free RL algorithms based on $\kappa$-PI and $\kappa$-VI in which the surrogate problem can be solved by any discrete or continuous action RL method, such as DQN and TRPO. We identify the importance of a hyper-parameter that controls the extent to which the surrogate problem is solved and suggest a way to set this parameter. When evaluated on a range of Atari and MuJoCo benchmark tasks, our results indicate that for the right range of $\kappa$, our algorithms outperform DQN and TRPO. This shows that our multi-step greedy algorithms are general enough to be applied over any existing RL algorithm and can significantly improve its performance., Comment: ICML 2020