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Learning representations of underlying environmental dynamics from partial observations is a critical challenge in machine learning. In the context of Partially Observable Markov Decision Processes (POMDPs), state representations are often inferred from the history of past observations and actions. We demonstrate that incorporating future information is essential to accurately capture causal dynamics and enhance state representations. To address this, we introduce a Dynamical Variational Auto-Encoder (DVAE) designed to learn causal Markovian dynamics from offline trajectories in a POMDP. Our method employs an extended hindsight framework that integrates past, current, and multi-step future information within a factored-POMDP setting. Empirical results reveal that this approach uncovers the causal graph governing hidden state transitions more effectively than history-based and typical hindsight-based models.

Pure exploration in bandits models multiple real-world problems, such as tuning hyper-parameters or conducting user studies, where different safety, resource, and fairness constraints on the decision space naturally appear. We study these problems as pure exploration in multi-armed bandits with unknown linear constraints, where the aim is to identify an $r$$\textit{-good feasible policy}$. First, we propose a Lagrangian relaxation of the sample complexity lower bound for pure exploration under constraints. We show how this lower bound evolves with the sequential estimation of constraints. Second, we leverage the Lagrangian lower bound and the properties of convex optimisation to propose two computationally efficient extensions of Track-and-Stop and Gamified Explorer, namely LATS and LAGEX. To this end, we propose a constraint-adaptive stopping rule, and while tracking the lower bound, use pessimistic estimate of the feasible set at each step. We show that these algorithms achieve asymptotically optimal sample complexity upper bounds up to constraint-dependent constants. Finally, we conduct numerical experiments with different reward distributions and constraints that validate efficient performance of LAGEX and LATS with respect to baselines.

With the pervasive deployment of Machine Learning (ML) models in real-world applications, verifying and auditing properties of ML models have become a central concern. In this work, we focus on three properties: robustness, individual fairness, and group fairness. We discuss two approaches for auditing ML model properties: estimation with and without reconstruction of the target model under audit. Though the first approach is studied in the literature, the second approach remains unexplored. For this purpose, we develop a new framework that quantifies different properties in terms of the Fourier coefficients of the ML model under audit but does not parametrically reconstruct it. We propose the Active Fourier Auditor (AFA), which queries sample points according to the Fourier coefficients of the ML model, and further estimates the properties. We derive high probability error bounds on AFA's estimates, along with the worst-case lower bounds on the sample complexity to audit them. Numerically we demonstrate on multiple datasets and models that AFA is more accurate and sample-efficient to estimate the properties of interest than the baselines.

Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a task-based approach and aim to understand whether a certain data analysis tool, like linear regression, would yield similar answers both on the population and the sample survey. In this paper, we design an algorithm to test the credibility of a sample survey in terms of linear regression. In other words, we design an algorithm that can certify if a sample survey is good enough to guarantee the correctness of data analysis done using linear regression tools. Nowadays, one is naturally concerned about data privacy in surveys. Thus, we further test the credibility of surveys published in a differentially private manner. Specifically, we focus on Local Differential Privacy (LDP), which is a standard technique to ensure privacy in surveys where the survey participants might not trust the aggregator. We extend our algorithm to work even when the data analysis has been done using surveys with LDP. In the process, we also propose an algorithm that learns with high probability the guarantees a linear regression model on a survey published with LDP. Our algorithm also serves as a mechanism to learn linear regression models from data corrupted with noise coming from any subexponential distribution. We prove that it achieves the optimal estimation error bound for $\ell_1$ linear regression, which might be of broader interest. We prove the theoretical correctness of our algorithms while trying to reduce the sample complexity for both public and private surveys. We also numerically demonstrate the performance of our algorithms on real and synthetic datasets.

Capitalizing on the intuitive premise that shape characteristics are more robust to perturbations, we bridge adversarial graph learning with the emerging tools from computational topology, namely, persistent homology representations of graphs. We introduce the concept of witness complex to adversarial analysis on graphs, which allows us to focus only on the salient shape characteristics of graphs, yielded by the subset of the most essential nodes (i.e., landmarks), with minimal loss of topological information on the whole graph. The remaining nodes are then used as witnesses, governing which higher-order graph substructures are incorporated into the learning process. Armed with the witness mechanism, we design Witness Graph Topological Layer (WGTL), which systematically integrates both local and global topological graph feature representations, the impact of which is, in turn, automatically controlled by the robust regularized topological loss. Given the attacker's budget, we derive the important stability guarantees of both local and global topology encodings and the associated robust topological loss. We illustrate the versatility and efficiency of WGTL by its integration with five GNNs and three existing non-topological defense mechanisms. Our extensive experiments across six datasets demonstrate that WGTL boosts the robustness of GNNs across a range of perturbations and against a range of adversarial attacks, leading to relative gains of up to 18%.

Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation methods to tackle quantum few-body problems. In particular, variational methods have been proposed to ease numerical calculations and obtain precise solutions. One such method is the Stochastic Variational Method, which employs a stochastic search to determine the number and parameters of correlated Gaussian basis functions used to construct an ansatz of the wave function. Stochastic methods, however, face numerical and optimization challenges as the number of particles increases. We introduce a family of gradient variational methods that replace stochastic search with gradient optimization. We comparatively and empirically evaluate the performance of the baseline Stochastic Variational Method, several instances of the gradient variational method family, and some hybrid methods for selected few-body problems. We show that gradient and hybrid methods can be more efficient and effective than the Stochastic Variational Method. We discuss the role of singularities, oscillations, and gradient optimization strategies in the performance of the respective methods.

Deterministic policies are often preferred over stochastic ones when implemented on physical systems. They can prevent erratic and harmful behaviors while being easier to implement and interpret. However, in practice, exploration is largely performed by stochastic policies. First-order Bayesian Optimization (BO) methods offer a principled way of performing exploration using deterministic policies. This is done through a learned probabilistic model of the objective function and its gradient. Nonetheless, such approaches treat policy search as a black-box problem, and thus, neglect the reinforcement learning nature of the problem. In this work, we leverage the performance difference lemma to introduce a novel mean function for the probabilistic model. This results in augmenting BO methods with the action-value function. Hence, we call our method Augmented Bayesian Search~(ABS). Interestingly, this new mean function enhances the posterior gradient with the deterministic policy gradient, effectively bridging the gap between BO and policy gradient methods. The resulting algorithm combines the convenience of the direct policy search with the scalability of reinforcement learning. We validate ABS on high-dimensional locomotion problems and demonstrate competitive performance compared to existing direct policy search schemes., Comment: Accepted to the International Conference on Learning Representations (ICLR) 2024

Best Arm Identification (BAI) problems are progressively used for data-sensitive applications, such as designing adaptive clinical trials, tuning hyper-parameters, and conducting user studies. Motivated by the data privacy concerns invoked by these applications, we study the problem of BAI with fixed confidence in both the local and central models, i.e. $\epsilon$-local and $\epsilon$-global Differential Privacy (DP). First, to quantify the cost of privacy, we derive lower bounds on the sample complexity of any $\delta$-correct BAI algorithm satisfying $\epsilon$-global DP or $\epsilon$-local DP. Our lower bounds suggest the existence of two privacy regimes. In the high-privacy regime, the hardness depends on a coupled effect of privacy and novel information-theoretic quantities involving the Total Variation. In the low-privacy regime, the lower bounds reduce to the non-private lower bounds. We propose $\epsilon$-local DP and $\epsilon$-global DP variants of a Top Two algorithm, namely CTB-TT and AdaP-TT*, respectively. For $\epsilon$-local DP, CTB-TT is asymptotically optimal by plugging in a private estimator of the means based on Randomised Response. For $\epsilon$-global DP, our private estimator of the mean runs in arm-dependent adaptive episodes and adds Laplace noise to ensure a good privacy-utility trade-off. By adapting the transportation costs, the expected sample complexity of AdaP-TT* reaches the asymptotic lower bound up to multiplicative constants., Comment: arXiv admin note: substantial text overlap with arXiv:2309.02202

High dimensional sparse linear bandits serve as an efficient model for sequential decision-making problems (e.g. personalized medicine), where high dimensional features (e.g. genomic data) on the users are available, but only a small subset of them are relevant. Motivated by data privacy concerns in these applications, we study the joint differentially private high dimensional sparse linear bandits, where both rewards and contexts are considered as private data. First, to quantify the cost of privacy, we derive a lower bound on the regret achievable in this setting. To further address the problem, we design a computationally efficient bandit algorithm, \textbf{F}orgetfu\textbf{L} \textbf{I}terative \textbf{P}rivate \textbf{HA}rd \textbf{T}hresholding (FLIPHAT). Along with doubling of episodes and episodic forgetting, FLIPHAT deploys a variant of Noisy Iterative Hard Thresholding (N-IHT) algorithm as a sparse linear regression oracle to ensure both privacy and regret-optimality. We show that FLIPHAT achieves optimal regret in terms of privacy parameters $\epsilon, \delta$, context dimension $d$, and time horizon $T$ up to a linear factor in model sparsity and logarithmic factor in $d$. We analyze the regret by providing a novel refined analysis of the estimation error of N-IHT, which is of parallel interest., Comment: 31 pages, 3 figures

Federated Learning (FL) is a collaborative machine learning (ML) approach, where multiple clients participate in training an ML model without exposing the private data. Fair and accurate assessment of client contributions is an important problem in FL to facilitate incentive allocation and encouraging diverse clients to participate in a unified model training. Existing methods for assessing client contribution adopts co-operative game-theoretic concepts, such as Shapley values, but under simplified assumptions. In this paper, we propose a history-aware game-theoretic framework, called FLContrib, to assess client contributions when a subset of (potentially non-i.i.d.) clients participate in each epoch of FL training. By exploiting the FL training process and linearity of Shapley value, we develop FLContrib that yields a historical timeline of client contributions as FL training progresses over epochs. Additionally, to assess client contribution under limited computational budget, we propose a scheduling procedure that considers a two-sided fairness criteria to perform expensive Shapley value computation only in a subset of training epochs. In experiments, we demonstrate a controlled trade-off between the correctness and efficiency of client contributions assessed via FLContrib. To demonstrate the benefits of history-aware client contributions, we apply FLContrib to detect dishonest clients conducting data poisoning in FL training., Comment: Under submission

We study the per-datum Membership Inference Attacks (MIAs), where an attacker aims to infer whether a fixed target datum has been included in the input dataset of an algorithm and thus, violates privacy. First, we define the membership leakage of a datum as the advantage of the optimal adversary targeting to identify it. Then, we quantify the per-datum membership leakage for the empirical mean, and show that it depends on the Mahalanobis distance between the target datum and the data-generating distribution. We further assess the effect of two privacy defences, i.e. adding Gaussian noise and sub-sampling. We quantify exactly how both of them decrease the per-datum membership leakage. Our analysis builds on a novel proof technique that combines an Edgeworth expansion of the likelihood ratio test and a Lindeberg-Feller central limit theorem. Our analysis connects the existing likelihood ratio and scalar product attacks, and also justifies different canary selection strategies used in the privacy auditing literature. Finally, our experiments demonstrate the impacts of the leakage score, the sub-sampling ratio and the noise scale on the per-datum membership leakage as indicated by the theory.

The rising successes of RL are propelled by combining smart algorithmic strategies and deep architectures to optimize the distribution of returns and visitations over the state-action space. A quantitative framework to compare the learning processes of these eclectic RL algorithms is currently absent but desired in practice. We address this gap by representing the learning process of an RL algorithm as a sequence of policies generated during training, and then studying the policy trajectory induced in the manifold of state-action occupancy measures. Using an optimal transport-based metric, we measure the length of the paths induced by the policy sequence yielded by an RL algorithm between an initial policy and a final optimal policy. Hence, we first define the 'Effort of Sequential Learning' (ESL). ESL quantifies the relative distance that an RL algorithm travels compared to the shortest path from the initial to the optimal policy. Further, we connect the dynamics of policies in the occupancy measure space and regret (another metric to understand the suboptimality of an RL algorithm), by defining the 'Optimal Movement Ratio' (OMR). OMR assesses the fraction of movements in the occupancy measure space that effectively reduce an analogue of regret. Finally, we derive approximation guarantees to estimate ESL and OMR with finite number of samples and without access to an optimal policy. Through empirical analyses across various environments and algorithms, we demonstrate that ESL and OMR provide insights into the exploration processes of RL algorithms and hardness of different tasks in discrete and continuous MDPs.