Swetha Ganesh

Swetha Ganesh, Washim Uddin Mondal, Vaneet Aggarwal

This work examines average-reward reinforcement learning with general policy parametrization. Existing state-of-the-art (SOTA) guarantees for this problem are either suboptimal or hindered by several challenges, including poor scalability with respect to the size of the state-action space, high iteration complexity, and dependence on knowledge of mixing times and hitting times. To address these limitations, we propose a Multi-level Monte Carlo-based Natural Actor-Critic (MLMC-NAC) algorithm. Our work is the first to achieve a global convergence rate of $\tilde{\mathcal{O}}(1/\sqrt{T})$ for average-reward Markov Decision Processes (MDPs) (where $T$ is the horizon length), without requiring the knowledge of mixing and hitting times. Moreover, the convergence rate does not scale with the size of the state space, therefore even being applicable to infinite state spaces.

Swetha Ganesh, Alexandre Reiffers-Masson, Gugan Thoppe

We introduce an observation-matrix-based framework for fully asynchronous online Federated Learning (FL) with adversaries. In this work, we demonstrate its effectiveness in estimating the mean of a random vector. Our main result is that the proposed algorithm almost surely converges to the desired mean $μ.$ This makes ours the first asynchronous FL method to have an a.s. convergence guarantee in the presence of adversaries. We derive this convergence using a novel differential-inclusion-based two-timescale analysis. Two other highlights of our proof include (a) the use of a novel Lyapunov function to show that $μ$ is the unique global attractor for our algorithm's limiting dynamics, and (b) the use of martingale and stopping-time theory to show that our algorithm's iterates are almost surely bounded.

Anirudh Satheesh, Sooraj Sathish, Swetha Ganesh et al.

In this work, we study the problem of finding robust and safe policies in Robust Constrained Average-Cost Markov Decision Processes (RCMDPs). A key challenge in this setting is the lack of strong duality, which prevents the direct use of standard primal-dual methods for constrained RL. Additional difficulties arise from the average-cost setting, where the Robust Bellman operator is not a contraction under any norm. To address these challenges, we propose an actor-critic algorithm for Average-Cost RCMDPs. We show that our method achieves both \(ε\)-feasibility and \(ε\)-optimality, and we establish a sample complexities of \(\tilde{O}\left(ε^{-4}\right)\) and \(\tilde{O}\left(ε^{-6}\right)\) with and without slackness assumption, which is comparable to the discounted setting.

Anik Kumar Paul, Nibedita Roy, Nagesh Talagani et al.

We propose FAR-SIGN (Fully Asynchronous Robust optimization via SIGNed directional projections) for adversary-resilient learning in parameter-server--worker systems. FAR-SIGN achieves robustness through sign-based updates along carefully designed directions and mitigates the resulting bias via a two-timescale mechanism. It admits both first-order and zeroth-order implementations and enables fully asynchronous execution without requiring a private reference dataset at the server. We establish almost-sure convergence of FAR-SIGN to the set of stationary points for smooth, nonconvex objectives. Moreover, we prove the near-optimal rate of $O(n^{-1/4+ε})$ in the first-order setting and the standard $O(n^{-1/6+ε})$ in the zeroth-order setting, where $n$ is the iteration count and $ε>0$ can be chosen arbitrarily small. Experiments on MNIST show that FAR-SIGN outperforms robust aggregation-based methods in both accuracy and wall-clock time.

Swetha Ganesh, Washim Uddin Mondal, Vaneet Aggarwal

We present two Policy Gradient-based algorithms with general parametrization in the context of infinite-horizon average reward Markov Decision Process (MDP). The first one employs Implicit Gradient Transport for variance reduction, ensuring an expected regret of the order $\tilde{\mathcal{O}}(T^{2/3})$. The second approach, rooted in Hessian-based techniques, ensures an expected regret of the order $\tilde{\mathcal{O}}(\sqrt{T})$. These results significantly improve the state-of-the-art $\tilde{\mathcal{O}}(T^{3/4})$ regret and achieve the theoretical lower bound. We also show that the average-reward function is approximately $L$-smooth, a result that was previously assumed in earlier works.

Swetha Ganesh, Jiayu Chen, Gugan Thoppe et al.

Federated Reinforcement Learning (FRL) allows multiple agents to collaboratively build a decision making policy without sharing raw trajectories. However, if a small fraction of these agents are adversarial, it can lead to catastrophic results. We propose a policy gradient based approach that is robust to adversarial agents which can send arbitrary values to the server. Under this setting, our results form the first global convergence guarantees with general parametrization. These results demonstrate resilience with adversaries, while achieving optimal sample complexity of order $\tilde{\mathcal{O}}\left( \frac{1}{Nε^2} \left( 1+ \frac{f^2}{N}\right)\right)$, where $N$ is the total number of agents and $f<N/2$ is the number of adversarial agents.

Yang Xu, Swetha Ganesh, Vaneet Aggarwal

We present a non-asymptotic convergence analysis of $Q$-learning and actor-critic algorithms for robust average-reward Markov Decision Processes (MDPs) under contamination, total-variation (TV) distance, and Wasserstein uncertainty sets. A key ingredient of our analysis is showing that the optimal robust $Q$ operator is a strict contraction with respect to a carefully designed semi-norm (with constant functions quotiented out). This property enables a stochastic approximation update that learns the optimal robust $Q$-function using $\tilde{\mathcal{O}}(ε^{-2})$ samples. We also provide an efficient routine for robust $Q$-function estimation, which in turn facilitates robust critic estimation. Building on this, we introduce an actor-critic algorithm that learns an $ε$-optimal robust policy within $\tilde{\mathcal{O}}(ε^{-2})$ samples. We provide numerical simulations to evaluate the performance of our algorithms.

Yang Xu, Swetha Ganesh, Washim Uddin Mondal et al.

This paper investigates infinite-horizon average reward Constrained Markov Decision Processes (CMDPs) with general parametrization. We propose a Primal-Dual Natural Actor-Critic algorithm that adeptly manages constraints while ensuring a high convergence rate. In particular, our algorithm achieves global convergence and constraint violation rates of $\tilde{\mathcal{O}}(1/\sqrt{T})$ over a horizon of length $T$ when the mixing time, $τ_{\mathrm{mix}}$, is known to the learner. In absence of knowledge of $τ_{\mathrm{mix}}$, the achievable rates change to $\tilde{\mathcal{O}}(1/T^{0.5-ε})$ provided that $T \geq \tilde{\mathcal{O}}\left(τ_{\mathrm{mix}}^{2/ε}\right)$. Our results match the theoretical lower bound for Markov Decision Processes and establish a new benchmark in the theoretical exploration of average reward CMDPs.

Swetha Ganesh, Rohan Deb, Gugan Thoppe et al.

Stochastic Heavy Ball (SHB) and Nesterov's Accelerated Stochastic Gradient (ASG) are popular momentum methods in stochastic optimization. While benefits of such acceleration ideas in deterministic settings are well understood, their advantages in stochastic optimization is still unclear. In fact, in some specific instances, it is known that momentum does not help in the sample complexity sense. Our work shows that a similar outcome actually holds for the whole of quadratic optimization. Specifically, we obtain a lower bound on the sample complexity of SHB and ASG for this family and show that the same bound can be achieved by the vanilla SGD. We note that there exist results claiming the superiority of momentum based methods in quadratic optimization, but these are based on one-sided or flawed analyses.