arXiv subjects

Ambuj Tewari

Publications and source records attributed to Ambuj Tewari.

At least 73 records · Page 4Linked to original sources

arXiv2023

Offline Policy Evaluation and Optimization under Confounding

Evaluating and optimizing policies in the presence of unobserved confounders is a problem of growing interest in offline reinforcement learning. Using conventional methods for offline RL in the presence of confounding can not only lead to poor decisions and poor policies, but also have disastrous effects in critical applications such as healthcare and education. We map out the landscape of offline policy evaluation for confounded MDPs, distinguishing assumptions on confounding based on whether they are memoryless and on their effect on the data-collection policies. We characterize settings where consistent value estimates are provably not achievable, and provide algorithms with guarantees to instead estimate lower bounds on the value. When consistent estimates are achievable, we provide algorithms for value estimation with sample complexity guarantees. We also present new algorithms for offline policy improvement and prove local convergence guarantees. Finally, we experimentally evaluate our algorithms on both a gridworld environment and a simulated healthcare setting of managing sepsis patients. In gridworld, our model-based method provides tighter lower bounds than existing methods, while in the sepsis simulator, our methods significantly outperform confounder-oblivious benchmarks.

stat.ML↗

arXiv2023

A Primal-Dual-Critic Algorithm for Offline Constrained Reinforcement Learning

Offline constrained reinforcement learning (RL) aims to learn a policy that maximizes the expected cumulative reward subject to constraints on expected cumulative cost using an existing dataset. In this paper, we propose Primal-Dual-Critic Algorithm (PDCA), a novel algorithm for offline constrained RL with general function approximation. PDCA runs a primal-dual algorithm on the Lagrangian function estimated by critics. The primal player employs a no-regret policy optimization oracle to maximize the Lagrangian estimate and the dual player acts greedily to minimize the Lagrangian estimate. We show that PDCA can successfully find a near saddle point of the Lagrangian, which is nearly optimal for the constrained RL problem. Unlike previous work that requires concentrability and a strong Bellman completeness assumption, PDCA only requires concentrability and realizability assumptions for sample-efficient learning.

cs.LG↗

arXiv2023

Sequence Length Independent Norm-Based Generalization Bounds for Transformers

This paper provides norm-based generalization bounds for the Transformer architecture that do not depend on the input sequence length. We employ a covering number based approach to prove our bounds. We use three novel covering number bounds for the function class of bounded linear transformations to upper bound the Rademacher complexity of the Transformer. Furthermore, we show this generalization bound applies to the common Transformer training technique of masking and then predicting the masked word. We also run a simulated study on a sparse majority data set that empirically validates our theoretical findings.

stat.ML↗

arXiv2023

Conformal Contextual Robust Optimization

Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative uncertainty regions, often resulting in suboptimal decisionmaking. To this end, we propose Conformal-Predict-Then-Optimize (CPO), a framework for leveraging highly informative, nonconvex conformal prediction regions over high-dimensional spaces based on conditional generative models, which have the desired distribution-free coverage guarantees. Despite guaranteeing robustness, such black-box optimization procedures alone inspire little confidence owing to the lack of explanation of why a particular decision was found to be optimal. We, therefore, augment CPO to additionally provide semantically meaningful visual summaries of the uncertainty regions to give qualitative intuition for the optimal decision. We highlight the CPO framework by demonstrating results on a suite of simulation-based inference benchmark tasks and a vehicle routing task based on probabilistic weather prediction.

stat.ME↗

arXiv2023

High-dimensional variable selection with heterogeneous signals: A precise asymptotic perspective

We study the problem of exact support recovery for high-dimensional sparse linear regression under independent Gaussian design when the signals are weak, rare, and possibly heterogeneous. Under a suitable scaling of the sample size and signal sparsity, we fix the minimum signal magnitude at the information-theoretic optimal rate and investigate the asymptotic selection accuracy of best subset selection (BSS) and marginal screening (MS) procedures. We show that despite the ideal setup, somewhat surprisingly, marginal screening can fail to achieve exact recovery with probability converging to one in the presence of heterogeneous signals, whereas BSS enjoys model consistency whenever the minimum signal strength is above the information-theoretic threshold. To mitigate the computational intractability of BSS, we also propose an efficient two-stage algorithmic framework called ETS (Estimate Then Screen) comprised of an estimation step and gradient coordinate screening step, and under the same scaling assumption on sample size and sparsity, we show that ETS achieves model consistency under the same information-theoretic optimal requirement on the minimum signal strength as BSS. Finally, we present a simulation study comparing ETS with LASSO and marginal screening. The numerical results agree with our asymptotic theory even for realistic values of the sample size, dimension and sparsity.

math.ST↗

arXiv2023

Multiclass Online Learning and Uniform Convergence

We study multiclass classification in the agnostic adversarial online learning setting. As our main result, we prove that any multiclass concept class is agnostically learnable if and only if its Littlestone dimension is finite. This solves an open problem studied by Daniely, Sabato, Ben-David, and Shalev-Shwartz (2011,2015) who handled the case when the number of classes (or labels) is bounded. We also prove a separation between online learnability and online uniform convergence by exhibiting an easy-to-learn class whose sequential Rademacher complexity is unbounded. Our learning algorithm uses the multiplicative weights algorithm, with a set of experts defined by executions of the Standard Optimal Algorithm on subsequences of size Littlestone dimension. We argue that the best expert has regret at most Littlestone dimension relative to the best concept in the class. This differs from the well-known covering technique of Ben-David, Pál, and Shalev-Shwartz (2009) for binary classification, where the best expert has regret zero.

cs.LG↗

arXiv2023

On Proper Learnability between Average- and Worst-case Robustness

Recently, Montasser et al. [2019] showed that finite VC dimension is not sufficient for proper adversarially robust PAC learning. In light of this hardness, there is a growing effort to study what type of relaxations to the adversarially robust PAC learning setup can enable proper learnability. In this work, we initiate the study of proper learning under relaxations of the worst-case robust loss. We give a family of robust loss relaxations under which VC classes are properly PAC learnable with sample complexity close to what one would require in the standard PAC learning setup. On the other hand, we show that for an existing and natural relaxation of the worst-case robust loss, finite VC dimension is not sufficient for proper learning. Lastly, we give new generalization guarantees for the adversarially robust empirical risk minimizer.

cs.LG↗

arXiv2023

On the Learnability of Multilabel Ranking

Multilabel ranking is a central task in machine learning. However, the most fundamental question of learnability in a multilabel ranking setting with relevance-score feedback remains unanswered. In this work, we characterize the learnability of multilabel ranking problems in both batch and online settings for a large family of ranking losses. Along the way, we give two equivalence classes of ranking losses based on learnability that capture most, if not all, losses used in practice.

cs.LG↗

arXiv2023

An Optimization-based Algorithm for Non-stationary Kernel Bandits without Prior Knowledge

We propose an algorithm for non-stationary kernel bandits that does not require prior knowledge of the degree of non-stationarity. The algorithm follows randomized strategies obtained by solving optimization problems that balance exploration and exploitation. It adapts to non-stationarity by restarting when a change in the reward function is detected. Our algorithm enjoys a tighter dynamic regret bound than previous work on the non-stationary kernel bandit setting. Moreover, when applied to the non-stationary linear bandit setting by using a linear kernel, our algorithm is nearly minimax optimal, solving an open problem in the non-stationary linear bandit literature. We extend our algorithm to use a neural network for dynamically adapting the feature mapping to observed data. We prove a dynamic regret bound of the extension using the neural tangent kernel theory. We demonstrate empirically that our algorithm and the extension can adapt to varying degrees of non-stationarity.

stat.ML↗

arXiv2023

Learning Mixtures of Markov Chains and MDPs

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a multi-step process, involving (1) a subspace estimation step, (2) spectral clustering of trajectories using "pairwise distance estimators," along with refinement using the EM algorithm, (3) a model estimation step, and (4) a classification step for predicting labels of new trajectories. We provide end-to-end performance guarantees, where we only explicitly require the length of trajectories to be linear in the number of states and the number of trajectories to be linear in a mixing time parameter. Experimental results support these guarantees, where we attain 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming the EM algorithm with random initialization (73.2% average accuracy).

stat.ML↗

arXiv2023

Thompson Sampling for High-Dimensional Sparse Linear Contextual Bandits

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

stat.ML↗

arXiv2023

Adaptive Sampling for Discovery

In this paper, we study a sequential decision-making problem, called Adaptive Sampling for Discovery (ASD). Starting with a large unlabeled dataset, algorithms for ASD adaptively label the points with the goal to maximize the sum of responses. This problem has wide applications to real-world discovery problems, for example drug discovery with the help of machine learning models. ASD algorithms face the well-known exploration-exploitation dilemma. The algorithm needs to choose points that yield information to improve model estimates but it also needs to exploit the model. We rigorously formulate the problem and propose a general information-directed sampling (IDS) algorithm. We provide theoretical guarantees for the performance of IDS in linear, graph and low-rank models. The benefits of IDS are shown in both simulation experiments and real-data experiments for discovering chemical reaction conditions.

stat.ML↗

arXiv2022

RL Boltzmann Generators for Conformer Generation in Data-Sparse Environments

The generation of conformers has been a long-standing interest to structural chemists and biologists alike. A subset of proteins known as intrinsically disordered proteins (IDPs) fail to exhibit a fixed structure and, therefore, must also be studied in this light of conformer generation. Unlike in the small molecule setting, ground truth data are sparse in the IDP setting, undermining many existing conformer generation methods that rely on such data for training. Boltzmann generators, trained solely on the energy function, serve as an alternative but display a mode collapse that similarly preclude their direct application to IDPs. We investigate the potential of training an RL Boltzmann generator against a closely related "Gibbs score," and demonstrate that conformer coverage does not track well with such training. This suggests that the inadequacy of solely training against the energy is independent of the modeling modality

q-bio.QM↗

arXiv2022

Online Agnostic Multiclass Boosting

Boosting is a fundamental approach in machine learning that enjoys both strong theoretical and practical guarantees. At a high-level, boosting algorithms cleverly aggregate weak learners to generate predictions with arbitrarily high accuracy. In this way, boosting algorithms convert weak learners into strong ones. Recently, Brukhim et al. extended boosting to the online agnostic binary classification setting. A key ingredient in their approach is a clean and simple reduction to online convex optimization, one that efficiently converts an arbitrary online convex optimizer to an agnostic online booster. In this work, we extend this reduction to multiclass problems and give the first boosting algorithm for online agnostic mutliclass classification. Our reduction also enables the construction of algorithms for statistical agnostic, online realizable, and statistical realizable multiclass boosting.

cs.LG↗

arXiv2022

Learning in Online MDPs: Is there a Price for Handling the Communicating Case?

It is a remarkable fact that the same $O(\sqrt{T})$ regret rate can be achieved in both the Experts Problem and the Adversarial Multi-Armed Bandit problem albeit with a worse dependence on number of actions in the latter case. In contrast, it has been shown that handling online MDPs with communicating structure and bandit information incurs $Ω(T^{2/3})$ regret even in the case of deterministic transitions. Is this the price we pay for handling communicating structure or is it because we also have bandit feedback? In this paper we show that with full information, online MDPs can still be learned at an $O(\sqrt{T})$ rate even in the presence of communicating structure. We first show this by proposing an efficient follow the perturbed leader (FPL) algorithm for the deterministic transition case. We then extend our scope to consider stochastic transitions where we first give an inefficient $O(\sqrt{T})$-regret algorithm (with a mild additional condition on the dynamics). Then we show how to achieve $O\left(\sqrt{\frac{T}α}\right)$ regret rate using an oracle-efficient algorithm but with the additional restriction that the starting state distribution has mass at least $α$ on each state.

cs.LG↗

arXiv2022

Generalization Bounds in the Predict-then-Optimize Framework

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted parameters, in contrast to the prediction error of the parameters. This loss function was recently introduced in Elmachtoub and Grigas (2022) and referred to as the Smart Predict-then-Optimize (SPO) loss. In this work, we seek to provide bounds on how well the performance of a prediction model fit on training data generalizes out-of-sample, in the context of the SPO loss. Since the SPO loss is non-convex and non-Lipschitz, standard results for deriving generalization bounds do not apply. We first derive bounds based on the Natarajan dimension that, in the case of a polyhedral feasible region, scale at most logarithmically in the number of extreme points, but, in the case of a general convex feasible region, have linear dependence on the decision dimension. By exploiting the structure of the SPO loss function and a key property of the feasible region, which we denote as the strength property, we can dramatically improve the dependence on the decision and feature dimensions. Our approach and analysis rely on placing a margin around problematic predictions that do not yield unique optimal solutions, and then providing generalization bounds in the context of a modified margin SPO loss function that is Lipschitz continuous. Finally, we characterize the strength property and show that the modified SPO loss can be computed efficiently for both strongly convex bodies and polytopes with an explicit extreme point representation.

cs.LG↗

arXiv2022

Balancing Adaptability and Non-exploitability in Repeated Games

We study the problem of guaranteeing low regret in repeated games against an opponent with unknown membership in one of several classes. We add the constraint that our algorithm is non-exploitable, in that the opponent lacks an incentive to use an algorithm against which we cannot achieve rewards exceeding some "fair" value. Our solution is an expert algorithm (LAFF) that searches within a set of sub-algorithms that are optimal for each opponent class and uses a punishment policy upon detecting evidence of exploitation by the opponent. With benchmarks that depend on the opponent class, we show that LAFF has sublinear regret uniformly over the possible opponents, except exploitative ones, for which we guarantee that the opponent has linear regret. To our knowledge, this work is the first to provide guarantees for both regret and non-exploitability in multi-agent learning.

cs.GT↗

arXiv2022

An Actor-Critic Contextual Bandit Algorithm for Personalized Mobile Health Interventions

Increasing technological sophistication and widespread use of smartphones and wearable devices provide opportunities for innovative and highly personalized health interventions. A Just-In-Time Adaptive Intervention (JITAI) uses real-time data collection and communication capabilities of modern mobile devices to deliver interventions in real-time that are adapted to the in-the-moment needs of the user. The lack of methodological guidance in constructing data-based JITAIs remains a hurdle in advancing JITAI research despite the increasing popularity of JITAIs among clinical scientists. In this article, we make a first attempt to bridge this methodological gap by formulating the task of tailoring interventions in real-time as a contextual bandit problem. Interpretability requirements in the domain of mobile health lead us to formulate the problem differently from existing formulations intended for web applications such as ad or news article placement. Under the assumption of linear reward function, we choose the reward function (the "critic") parameterization separately from a lower dimensional parameterization of stochastic policies (the "actor"). We provide an online actor-critic algorithm that guides the construction and refinement of a JITAI. Asymptotic properties of the actor-critic algorithm are developed and backed up by numerical experiments. Additional numerical experiments are conducted to test the robustness of the algorithm when idealized assumptions used in the analysis of contextual bandit algorithm are breached.

stat.ML↗