One of the most basic problems in reinforcement learning (RL) is policy evaluation: estimating the long-term return, i.e., value function, corresponding to a given fixed policy. The celebrated Temporal Difference (TD) learning algorithm addresses this problem, and recent work has investigated finite-time convergence guarantees for this algorithm and variants thereof. However, these guarantees hinge on the reward observations being always generated from a well-behaved (e.g., sub-Gaussian) true reward distribution. Motivated by harsh, real-world environments where such an idealistic assumption may no longer hold, we revisit the policy evaluation problem from the perspective of \emph{adversarial robustness}. In particular, we consider a Huber-contaminated reward model where an adversary can arbitrarily corrupt each reward sample with a small probability $\epsilon$. Under this observation model, we first show that the adversary can cause the vanilla TD algorithm to converge to any arbitrary value function. We then develop a novel algorithm called \emph{Robust-TD} and prove that its finite-time guarantees match that of vanilla TD with linear function approximation up to a small $O(\epsilon)$ term that captures the effect of corruption. We complement this result with a minimax lower bound, revealing that such an additive corruption-induced term is unavoidable. To our knowledge, these results are the first of their kind in the context of adversarial robustness of stochastic approximation schemes driven by Markov noise. The key new technical tool that enables our results is an analysis of the Median-of-Means estimator with corrupted, time-correlated data that might be of independent interest to the literature on robust statistics.

Motivated by applications in large-scale and multi-agent reinforcement learning, we study the non-asymptotic performance of stochastic approximation (SA) schemes with delayed updates under Markovian sampling. While the effect of delays has been extensively studied for optimization, the manner in which they interact with the underlying Markov process to shape the finite-time performance of SA remains poorly understood. In this context, our first main contribution is to show that under time-varying bounded delays, the delayed SA update rule guarantees exponentially fast convergence of the \emph{last iterate} to a ball around the SA operator’s fixed point. Notably, our bound is \emph{tight} in its dependence on both the maximum delay $\tau_{max}$, and the mixing time $\tau_{mix}$. To achieve this tight bound, we develop a novel inductive proof technique that, unlike various existing delayed-optimization analyses, relies on establishing uniform boundedness of the iterates. As such, our proof may be of independent interest. Next, to mitigate the impact of the maximum delay on the convergence rate, we provide the first finite-time analysis of a delay-adaptive SA scheme under Markovian sampling. In particular, we show that the exponent of convergence of this scheme gets scaled down by $\tau_{avg}$, as opposed to $\tau_{max}$ for the vanilla delayed SA rule; here, $\tau_{avg}$ denotes the average delay across all iterations. Moreover, the adaptive scheme requires no prior knowledge of the delay sequence for step-size tuning. Our theoretical findings shed light on the finite-time effects of delays for a broad class of algorithms, including TD learning, Q-learning, and stochastic gradient descent under Markovian sampling.

Federated reinforcement learning (FRL) has emerged as a promising paradigm for reducing the sample complexity of reinforcement learning tasks by exploiting information from different agents. However, when each agent interacts with a potentially different environment, little to nothing is known theoretically about the non-asymptotic performance of FRL algorithms. The lack of such results can be attributed to various technical challenges and their intricate interplay: Markovian sampling, linear function approximation, multiple local updates to save communication, heterogeneity in the reward functions and transition kernels of the agents' MDPs, and continuous state-action spaces. Moreover, in the on-policy setting, the behavior policies vary with time, further complicating the analysis. In response, we introduce FedSARSA, a novel federated on-policy reinforcement learning scheme, equipped with linear function approximation, to address these challenges and provide a comprehensive finite-time error analysis. Notably, we establish that FedSARSA converges to a policy that is near-optimal for all agents, with the extent of near-optimality proportional to the level of heterogeneity. Furthermore, we prove that FedSARSA leverages agent collaboration to enable linear speedups as the number of agents increases, which holds for both fixed and adaptive step-size configurations.

Designing distributed control systems (DCS) is challenging because we need to balance the application control performance with the real-time hardware resource costs. Compared to the abundance of automated tools for monolithic systems, managing the design and implementation of DCS still heavily relies on human expertise. To address this challenge, we propose a human-augmenting design tool that suggests and explores tradeoffs in co-optimizing controller simplification and multiprocessor distributed task scheduling with a simple dial. Our work creatively combines sparsity-based optimal controller simplification with task consolidation, to achieve an optimal control performance on the smallest distributed hardware footprint. Our unique task consolidator adapts to various real-time scheduling algorithms and allocates control tasks to the fewest nodes under the utilization bounds of the chosen real-time scheduler. To account for real-time guarantees when assigning the controller, we introduce an improved worst-case execution time (WCET) model based on a mixed Weibull distribution. This new WCET model provides state-of-the-art accuracy of WCET based upon fewer data samples, thus reducing design-time effort and improving run-time performance. With our tool, designers can virtually simulate the theoretical optimum, physically download it, or experimentally explore alternative tradeoffs between system cost and controller performance. In a real-world implementation, our tool reduced 60% of hardware costs by trading off merely 0.14% of control performance. By automating the “simplification – demux – WCET estimation – task consolidation” pipeline, our tool allows control engineers to balance control performance and system cost directly, speeding up manual distributed controller design by 16 times.

We consider a linear stochastic bandit problem involving $M$ agents that can collaborate via a central server to minimize regret. A fraction $\alpha$ of these agents are adversarial and can act arbitrarily, leading to the following tension: while collaboration can potentially reduce regret, it can also disrupt the process of learning due to adversaries. In this work, we provide a fundamental understanding of this tension by designing new algorithms that balance the exploration-exploitation trade-off via carefully constructed robust confidence intervals. We also complement our algorithms with tight analyses. First, we develop a robust collaborative phased elimination algorithm that achieves $\tilde{O}\left(\alpha+ 1/\sqrt{M}\right) \sqrt{dT}$ regret for each good agent; here, $d$ is the model-dimension and $T$ is the horizon. For small $\alpha$, our result thus reveals a clear benefit of collaboration despite adversaries. Using an information-theoretic argument, we then prove a matching lower bound, thereby providing the first set of tight, near-optimal regret bounds for collaborative linear bandits with adversaries. Furthermore, by leveraging recent advances in high-dimensional robust statistics, we significantly extend our algorithmic ideas and results to (i) the generalized linear bandit model that allows for non-linear observation maps; and (ii) the contextual bandit setting that allows for time-varying feature vectors.

We consider a standard federated learning (FL) setup where a group of clients periodically coordinate with a central server to train a statistical model. We develop a general algorithmic framework called FedLin to tackle some of the key challenges intrinsic to FL, namely objective heterogeneity, systems heterogeneity, and infrequent and imprecise communication. Our framework is motivated by the observation that under these challenges, various existing FL algorithms suffer from a fundamental speed-accuracy conflict: they either guarantee linear convergence but to an incorrect point, or convergence to the global minimum but at a sub-linear rate, i.e., fast convergence comes at the expense of accuracy. In contrast, when the clients' local loss functions are smooth and strongly convex, we show that FedLin guarantees linear convergence to the global minimum, despite arbitrary objective and systems heterogeneity. We then establish matching upper and lower bounds on the convergence rate of FedLin that highlight the effects of infrequent, periodic communication. Finally, we show that FedLin preserves linear convergence rates under aggressive gradient sparsification, and quantify the effect of the compression level on the convergence rate. Notably, our work is the first to provide tight linear convergence rate guarantees, and constitutes the first comprehensive analysis of gradient sparsification in FL.

The concept of using a Magnetic Resonance Imaging (MRI) device for chemotherapy, by employing a micro robot, consisting of a polymer bound aggregate of ferromagnetic particles, is explored in this paper. We primarily contribute towards the design of a Fuzzy Sliding Mode Controller (FSMC) for trajectory tracking of the micro robot in the human vasculature considering a highly non-linear model available in literature. An adaptive algorithm based on Lyapunov stability theory is used to estimate the parameters associated with the FSMC. The proposed FSMC is able to eliminate the chattering phenomenon completely which is present in conventional sliding mode control. Since the system in consideration is a biological one, many parameters are difficult to estimate resulting in parametric uncertainties. A significant merit of the proposed framework is its ability to estimate the dielectric density of blood on-line with great accuracy. Simulation results also indicate perfect tracking with very fast dynamical response. To illustrate the efficacy of our controller, a detailed comparison is made between the performances of a state-of-the-art adaptive backstepping control and our proposed control action in the presence of bounded model uncertainties for micro-robots made up of different ferromagnetic materials.