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1. Breaking the sample complexity barrier to regret-optimal model-free reinforcement learning

   https://doi.org/10.1093/imaiai/iaac034  

   Li, Gen; Shi, Laixi; Chen, Yuxin; Chi, Yuejie (February 2023, Information and Inference: A Journal of the IMA)

   Abstract Achieving sample efficiency in online episodic reinforcement learning (RL) requires optimally balancing exploration and exploitation. When it comes to a finite-horizon episodic Markov decision process with $$S$$ states, $$A$$ actions and horizon length $$H$$, substantial progress has been achieved toward characterizing the minimax-optimal regret, which scales on the order of $$\sqrt{H^2SAT}$$ (modulo log factors) with $$T$$ the total number of samples. While several competing solution paradigms have been proposed to minimize regret, they are either memory-inefficient, or fall short of optimality unless the sample size exceeds an enormous threshold (e.g. $$S^6A^4 \,\mathrm{poly}(H)$$ for existing model-free methods). To overcome such a large sample size barrier to efficient RL, we design a novel model-free algorithm, with space complexity $O(SAH)$, that achieves near-optimal regret as soon as the sample size exceeds the order of $$SA\,\mathrm{poly}(H)$$. In terms of this sample size requirement (also referred to the initial burn-in cost), our method improves—by at least a factor of $S^5A^3$—upon any prior memory-efficient algorithm that is asymptotically regret-optimal. Leveraging the recently introduced variance reduction strategy (also called reference-advantage decomposition), the proposed algorithm employs an early-settled reference update rule, with the aid of two Q-learning sequences with upper and lower confidence bounds. The design principle of our early-settled variance reduction method might be of independent interest to other RL settings that involve intricate exploration–exploitation trade-offs. 

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2. Sample Amplification: Increasing Dataset Size even when Learning is Impossible

   Axelrod, Brian; Garg, Shivam; Sharan, Vatsal; Valiant, Gregory (January 2020, International Conference on Machine Learning (ICML))

   Given data drawn from an unknown distribution, D, to what extent is it possible to ``amplify'' this dataset and faithfully output an even larger set of samples that appear to have been drawn from D? We formalize this question as follows: an (n,m) amplification procedure takes as input n independent draws from an unknown distribution D, and outputs a set of m > n ``samples'' which must be indistinguishable from m samples drawn iid from D. We consider this sample amplification problem in two fundamental settings: the case where D is an arbitrary discrete distribution supported on k elements, and the case where D is a d-dimensional Gaussian with unknown mean, and fixed covariance matrix. Perhaps surprisingly, we show a valid amplification procedure exists for both of these settings, even in the regime where the size of the input dataset, n, is significantly less than what would be necessary to learn distribution D to non-trivial accuracy. We also show that our procedures are optimal up to constant factors. Beyond these results, we describe potential applications of sample amplification, and formalize a number of curious directions for future research. 

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3. Sample Complexity of Robust Reinforcement Learning with a Generative Model

   Panaganti, Kishan; Kalathil, Dileep (March 2022, International Conference on Artificial Intelligence and Statistics (AISTATS))

   The Robust Markov Decision Process (RMDP) framework focuses on designing control policies that are robust against the parameter uncertainties due to the mis- matches between the simulator model and real-world settings. An RMDP problem is typically formulated as a max-min problem, where the objective is to find the policy that maximizes the value function for the worst possible model that lies in an uncertainty set around a nominal model. The standard robust dynamic programming approach requires the knowledge of the nominal model for computing the optimal robust policy. In this work, we propose a model-based reinforcement learning (RL) algorithm for learning an ε-optimal robust policy when the nominal model is unknown. We consider three different forms of uncertainty sets, characterized by the total variation distance, chi-square divergence, and KL divergence. For each of these uncertainty sets, we give a precise characterization of the sample complexity of our proposed algorithm. In addition to the sample complexity results, we also present a formal analytical argument on the benefit of using robust policies. Finally, we demonstrate the performance of our algorithm on two benchmark problems. 

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4. Sample Selection for Fair and Robust Training

   Roh, Yuji; Lee, Kangwook; Whang, Steven; Suh, Changho (January 2021, Advances in neural information processing systems)

   Ranzato, M.; Beygelzimer, A.; Liang, P.S.; Vaughan, J.W.; Dauphin, Y. (Ed.)

   Fairness and robustness are critical elements of Trustworthy AI that need to be addressed together. Fairness is about learning an unbiased model while robustness is about learning from corrupted data, and it is known that addressing only one of them may have an adverse affect on the other. In this work, we propose a sample selection-based algorithm for fair and robust training. To this end, we formulate a combinatorial optimization problem for the unbiased selection of samples in the presence of data corruption. Observing that solving this optimization problem is strongly NP-hard, we propose a greedy algorithm that is efficient and effective in practice. Experiments show that our method obtains fairness and robustness that are better than or comparable to the state-of-the-art technique, both on synthetic and benchmark real datasets. Moreover, unlike other fair and robust training baselines, our algorithm can be used by only modifying the sampling step in batch selection without changing the training algorithm or leveraging additional clean data. 

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5. Finite-Sample Bounds for Adaptive Inverse Reinforcement Learning Using Passive Langevin Dynamics

   https://doi.org/10.1109/TIT.2025.3555479  

   Snow, Luke; Krishnamurthy, Vikram (June 2025, IEEE Transactions on Information Theory)

   This paper provides a finite-sample analysis of a passive stochastic gradient Langevin dynamics (PSGLD) algo- rithm. This algorithm is designed to achieve adaptive inverse reinforcement learning (IRL). Adaptive IRL aims to estimate the cost function of a forward learner performing a stochastic gradient algorithm (e.g., policy gradient reinforcement learning) by observing their estimates in real-time. The PSGLD algorithm is considered passive because it incorporates noisy gradients provided by an external stochastic gradient algorithm (forward learner), of which it has no control. The PSGLD algorithm acts as a randomized sampler to achieve adaptive IRL by reconstructing the forward learner’s cost function nonparametrically from the stationary measure of a Langevin diffusion. This paper analyzes the non-asymptotic (finite-sample) performance; we provide explicit bounds on the 2-Wasserstein distance between PSGLD algorithm sample measure and the stationary measure encoding the cost function, and provide guarantees for a kernel density estimation scheme which reconstructs the cost function from empirical samples. Our analysis uses tools from the study of Markov diffusion operators. The derived bounds have both practical and theoretical significance. They provide finite-time guarantees for an adaptive IRL mechanism, and substantially generalize the analytical framework of a line of research in passive stochastic gradient algorithms. 

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