Load balancing and auto scaling are at the core of scalable, contemporary systems, addressing dynamic resource allocation and service rate adjustments in response to workload changes. This paper introduces a novel model and algorithms for tuning load balancers coupled with auto scalers, considering bursty traffic arriving at finite queues. We begin by presenting the problem as a weakly coupled Markov Decision Processes (MDP), solvable via a linear program (LP). However, as the number of control variables of such LP grows combinatorially, we introduce a more tractable relaxed LP formulation, and extend it to tackle the problem of online parameter learning and policy optimization using a two-timescale algorithm based on the LP Lagrangian.

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.

We tackle the problem of estimating the Value-at-Risk (VaR) and the Conditional Value-at-Risk (CVaR) of the infinite-horizon discounted cost within a Markov cost process. First, we derive a minimax lower bound of $\Omega(1/\sqrt{n})$ that holds both in an expected and in a probabilistic sense. Then, using a finite-horizon truncation scheme, we derive an upper bound for the error in CVaR estimation, which matches our lower bound up to constant factors. Finally, we discuss an extension of our estimation scheme that covers more general risk measures satisfying a certain continuity criterion, e.g., spectral risk measures, utility-based shortfall risk. To the best of our knowledge, our work is the first to provide lower and upper bounds on the estimation error for any risk measure within Markovian settings. We remark that our lower bounds also extend to the infinite-horizon discounted costs' mean. Even in that case, our result $\Omega(1/\sqrt{n}) $ improves upon the existing result $\Omega(1/n)$[13].

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 $\mu.$ 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 $\mu$ 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.

Evolution Strategy (ES) is a powerful black-box optimization technique based on the idea of natural evolution. In each of its iterations, a key step entails ranking candidate solutions based on some fitness score. For an ES method in Reinforcement Learning (RL), this ranking step requires evaluating multiple policies. This is presently done via on-policy approaches: each policy's score is estimated by interacting several times with the environment using that policy. This leads to a lot of wasteful interactions since, once the ranking is done, only the data associated with the top-ranked policies is used for subsequent learning. To improve sample efficiency, we propose a novel off-policy alternative for ranking, based on a local approximation for the fitness function. We demonstrate our idea in the context of a state-of-the-art ES method called the Augmented Random Search (ARS). Simulations in MuJoCo tasks show that, compared to the original ARS, our off-policy variant has similar running times for reaching reward thresholds but needs only around 70% as much data. It also outperforms the recent Trust Region ES. We believe our ideas should be extendable to other ES methods as well.

Q-learning and SARSA with $\epsilon$-greedy exploration are leading reinforcement learning methods. Their tabular forms converge to the optimal Q-function under reasonable conditions. However, with function approximation, these methods exhibit strange behaviors such as policy oscillation, chattering, and convergence to different attractors (possibly even the worst policy) on different runs, apart from the usual instability. A theory to explain these phenomena has been a long-standing open problem, even for basic linear function approximation (Sutton, 1999). Our work uses differential inclusion to provide the first framework for resolving this problem. We also provide numerical examples to illustrate our framework's prowess in explaining these algorithms' behaviors.

Despite the popularity of policy gradient methods, they are known to suffer from large variance and high sample complexity. To mitigate this, we introduce SoftTreeMax -- a generalization of softmax that takes planning into account. In SoftTreeMax, we extend the traditional logits with the multi-step discounted cumulative reward, topped with the logits of future states. We consider two variants of SoftTreeMax, one for cumulative reward and one for exponentiated reward. For both, we analyze the gradient variance and reveal for the first time the role of a tree expansion policy in mitigating this variance. We prove that the resulting variance decays exponentially with the planning horizon as a function of the expansion policy. Specifically, we show that the closer the resulting state transitions are to uniform, the faster the decay. In a practical implementation, we utilize a parallelized GPU-based simulator for fast and efficient tree search. Our differentiable tree-based policy leverages all gradients at the tree leaves in each environment step instead of the traditional single-sample-based gradient. We then show in simulation how the variance of the gradient is reduced by three orders of magnitude, leading to better sample complexity compared to the standard policy gradient. On Atari, SoftTreeMax demonstrates up to 5x better performance in a faster run time compared to distributed PPO. Lastly, we demonstrate that high reward correlates with lower variance.

For providing quick and accurate search results, a search engine maintains a local snapshot of the entire web. And, to keep this local cache fresh, it employs a crawler for tracking changes across various web pages. It would have been ideal if the crawler managed to update the local snapshot as soon as a page changed on the web. However, finite bandwidth availability and server restrictions mean that there is a bound on how frequently the different pages can be crawled. This then brings forth the following optimisation problem: maximise the freshness of the local cache subject to the crawling frequency being within the prescribed bounds. Recently, tractable algorithms have been proposed to solve this optimisation problem under different cost criteria. However, these assume the knowledge of exact page change rates, which is unrealistic in practice. We address this issue here. Specifically, we provide three novel schemes for online estimation of page change rates. All these schemes only need partial information about the page change process, i.e., they only need to know if the page has changed or not since the last crawl instance. Our first scheme is based on the law of large numbers, the second on the theory of stochastic approximation, while the third is an extension of the second and involves an additional momentum term. For all of these schemes, we prove convergence and, also, provide their convergence rates. As far as we know, the results concerning the third estimator is quite novel. Specifically, this is the first convergence type result for a stochastic approximation algorithm with momentum. Finally, we provide some numerical experiments (on real as well as synthetic data) to compare the performance of our proposed estimators with the existing ones (e.g., MLE).

TD(0) is one of the most commonly used algorithms in reinforcement learning. Despite this, there is no existing finite sample analysis for TD(0) with function approximation, even for the linear case. Our work is the first to provide such results. Existing convergence rates for Temporal Difference (TD) methods apply only to somewhat modified versions, e.g., projected variants or ones where stepsizes depend on unknown problem parameters. Our analyses obviate these artificial alterations by exploiting strong properties of TD(0). We provide convergence rates both in expectation and with high-probability. The two are obtained via different approaches that use relatively unknown, recently developed stochastic approximation techniques.

TD(0) is one of the most commonly used algorithms in reinforcement learning. Despite this, there is no existing finite sample analysis for TD(0) with function approximation, even for the linear case. Our work is the first to provide such results. Existing convergence rates for Temporal Difference (TD) methods apply only to somewhat modified versions, e.g., projected variants or ones where stepsizes depend on unknown problem parameters. Our analyses obviate these artificial alterations by exploiting strong properties of TD(0). We provide convergence rates both in expectation and with high-probability. The two are obtained via different approaches that use relatively unknown, recently developed stochastic approximation techniques.