arXiv subjects

Yashaswini Murthy

Publications and source records attributed to Yashaswini Murthy.

11 recordsLinked to original sources

arXiv2025

Finite-Time Convergence of Single-Trajectory Chi-Square Robust Q-Learning With Linear Function Approximation

Distributionally robust reinforcement learning seeks policies that remain effective when the deployment environment differs from the one that generated the training data. We study model-free robust Q-learning with $\chi^2$ uncertainty sets and linear function approximation, using data from a single trajectory of an unknown nominal MDP. Evaluating the $\chi^2$ robust Bellman target introduces the square root of a conditional second moment, which cannot be estimated unbiasedly from one transition, while the projected robust Bellman operator need not be contractive. We address these obstacles through a variational reformulation of the robust Bellman target and a blockwise frozen-target scheme, and establish a finite-time error bound relative to the optimal robust Q-function for every $\gamma\in(0,1)$. A neural-network experiment illustrates how the variational target can be used in a continuous-state nonlinear-control task.

cs.LG↗

arXiv2025

On the Gaussian Limit of the Output of IIR Filters

We study the asymptotic distribution of the output of a stable Linear Time-Invariant (LTI) system driven by a non-Gaussian stochastic input. Motivated by longstanding heuristics in the stochastic describing function method, we rigorously characterize when the output process becomes approximately Gaussian, even when the input is not. Using the Wasserstein-1 distance as a quantitative measure of non-Gaussianity, we derive upper bounds on the distance between the appropriately scaled output and a standard normal distribution. These bounds are obtained via Stein's method and depend explicitly on the system's impulse response and the dependence structure of the input process. We show that when the dominant pole of the system approaches the edge of stability and the input satisfies one of the following conditions: (i) independence, (ii) positive correlation with a real and positive dominant pole, or (iii) sufficient correlation decay, the output converges to a standard normal distribution at rate $O(1/\sqrt{t})$. We also present counterexamples where convergence fails, thereby motivating the stated assumptions. Our results provide a rigorous foundation for the widespread observation that outputs of low-pass LTI systems tend to be approximately Gaussian.

eess.SY↗

arXiv2024

Performance of NPG in Countable State-Space Average-Cost RL

We consider policy optimization methods in reinforcement learning settings where the state space is arbitrarily large, or even countably infinite. The motivation arises from control problems in communication networks, matching markets, and other queueing systems. Specifically, we consider the popular Natural Policy Gradient (NPG) algorithm, which has been studied in the past only under the assumption that the cost is bounded and the state space is finite, neither of which holds for the aforementioned control problems. Assuming a Lyapunov drift condition, which is naturally satisfied in some cases and can be satisfied in other cases at a small cost in performance, we design a state-dependent step-size rule which dramatically improves the performance of NPG for our intended applications. In addition to experimentally verifying the performance improvement, we also theoretically show that the iteration complexity of NPG can be made independent of the size of the state space. The key analytical tool we use is the connection between NPG step-sizes and the solution to Poisson's equation. In particular, we provide policy-independent bounds on the solution to Poisson's equation, which are then used to guide the choice of NPG step-sizes.

cs.LG↗

arXiv2024

On the Global Convergence of Policy Gradient in Average Reward Markov Decision Processes

We present the first finite time global convergence analysis of policy gradient in the context of infinite horizon average reward Markov decision processes (MDPs). Specifically, we focus on ergodic tabular MDPs with finite state and action spaces. Our analysis shows that the policy gradient iterates converge to the optimal policy at a sublinear rate of $O\left({\frac{1}{T}}\right),$ which translates to $O\left({\log(T)}\right)$ regret, where $T$ represents the number of iterations. Prior work on performance bounds for discounted reward MDPs cannot be extended to average reward MDPs because the bounds grow proportional to the fifth power of the effective horizon. Thus, our primary contribution is in proving that the policy gradient algorithm converges for average-reward MDPs and in obtaining finite-time performance guarantees. In contrast to the existing discounted reward performance bounds, our performance bounds have an explicit dependence on constants that capture the complexity of the underlying MDP. Motivated by this observation, we reexamine and improve the existing performance bounds for discounted reward MDPs. We also present simulations to empirically evaluate the performance of average reward policy gradient algorithm.

cs.LG↗

arXiv2023

On the Convergence of Modified Policy Iteration in Risk Sensitive Exponential Cost Markov Decision Processes

Modified policy iteration (MPI) is a dynamic programming algorithm that combines elements of policy iteration and value iteration. The convergence of MPI has been well studied in the context of discounted and average-cost MDPs. In this work, we consider the exponential cost risk-sensitive MDP formulation, which is known to provide some robustness to model parameters. Although policy iteration and value iteration have been well studied in the context of risk sensitive MDPs, MPI is unexplored. We provide the first proof that MPI also converges for the risk-sensitive problem in the case of finite state and action spaces. Since the exponential cost formulation deals with the multiplicative Bellman equation, our main contribution is a convergence proof which is quite different than existing results for discounted and risk-neutral average-cost problems as well as risk sensitive value and policy iteration approaches. We conclude our analysis with simulation results, assessing MPI's performance relative to alternative dynamic programming methods like value iteration and policy iteration across diverse problem parameters. Our findings highlight risk-sensitive MPI's enhanced computational efficiency compared to both value and policy iteration techniques.

cs.LG↗

arXiv2023

Performance Bounds for Policy-Based Average Reward Reinforcement Learning Algorithms

Many policy-based reinforcement learning (RL) algorithms can be viewed as instantiations of approximate policy iteration (PI), i.e., where policy improvement and policy evaluation are both performed approximately. In applications where the average reward objective is the meaningful performance metric, discounted reward formulations are often used with the discount factor being close to $1,$ which is equivalent to making the expected horizon very large. However, the corresponding theoretical bounds for error performance scale with the square of the horizon. Thus, even after dividing the total reward by the length of the horizon, the corresponding performance bounds for average reward problems go to infinity. Therefore, an open problem has been to obtain meaningful performance bounds for approximate PI and RL algorithms for the average-reward setting. In this paper, we solve this open problem by obtaining the first finite-time error bounds for average-reward MDPs, and show that the asymptotic error goes to zero in the limit as policy evaluation and policy improvement errors go to zero.

cs.LG↗

arXiv2022

A Policy Gradient Algorithm for the Risk-Sensitive Exponential Cost MDP

We study the risk-sensitive exponential cost MDP formulation and develop a trajectory-based gradient algorithm to find the stationary point of the cost associated with a set of parameterized policies. We derive a formula that can be used to compute the policy gradient from (state, action, cost) information collected from sample paths of the MDP for each fixed parameterized policy. Unlike the traditional average-cost problem, standard stochastic approximation theory cannot be used to exploit this formula. To address the issue, we introduce a truncated and smooth version of the risk-sensitive cost and show that this new cost criterion can be used to approximate the risk-sensitive cost and its gradient uniformly under some mild assumptions. We then develop a trajectory-based gradient algorithm to minimize the smooth truncated estimation of the risk-sensitive cost and derive conditions under which a sequence of truncations can be used to solve the original, untruncated cost problem.

eess.SY↗

arXiv2020

The Twelvefold Way of Non-Sequential Lossless Compression

Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invariances called the twelvefold way in enumerative combinatorics and develop a method to characterize lossless compression limits. Explicit computations for all twelve settings are carried out for i.i.d. uniform and Bernoulli distributions. Comparisons among settings provide quantitative insight.

cs.IT↗

arXiv2020

smartSDH: An Experimental Study of Mechanism Based Building Control

As Internet of Things (IoT) technologies are increasingly being deployed, situations frequently arise where multiple stakeholders must reconcile preferences to control a shared resource. We perform a 5-month long experiment dubbed 'smartSDH' (carried out in 27 employees' office space) where users report their preferences for the brightness of overhead lighting. smartSDH implements a modified Vickrey-Clarke-Groves (VCG) mechanism; assuming users are rational, it incentivizes truthful reporting, implements the socially desirable outcome, and compensates participants to ensure higher payoffs under smartSDH when compared with the default outside option(i.e., the option chosen in the absence of such a mechanism). smartSDH assesses the feasibility of the VCG mechanism in the context of smart building control and evaluated smartSDH's effect using metrics such as light level satisfaction, incentive satisfaction, and energy consumption. Although previous studies on the theoretical aspects of the mechanism indicate user satisfaction, our experiments indicate quite the contrary. We found that the participants were significantly less satisfied with light brightness and incentives determined by the VCG mechanism over time. These data suggest the need for more realistic behavioral models to design IoT technologies and highlights difficulties in estimating preferences from observable external factors such as atmospheric conditions.

cs.HC↗

arXiv2018

Nonlinear Dynamics of Binocular Rivalry: A Comparative Study

When our eyes are presented with the same image, the brain processes it to view it as a single coherent one. The lateral shift in the position of our eyes, causes the two images to possess certain differences, which our brain exploits for the purpose of depth perception and to gauge the size of objects at different distances, a process commonly known as stereopsis. However, when presented with two different visual stimuli, the visual awareness alternates. This phenomenon of binocular rivalry is a result of competition between the corresponding neuronal populations of the two eyes. The article presents a comparative study of various dynamical models proposed to capture this process. It goes on to study the effect of a certain parameter on the rate of perceptual alternations and proceeds to disprove the initial propositions laid down to characterise this phenomenon. It concludes with a discussion on the possible future work that can be conducted to obtain a better picture of the neuronal functioning behind this rivalry.

cs.NE↗

arXiv2018

A Lagrangian Model to Predict Microscallop Motion in non Newtonian Fluids

The need to develop models to predict the motion of microrobots, or robots of a much smaller scale, moving in fluids in a low Reynolds number regime, and in particular, in non Newtonian fluids, cannot be understated. The article develops a Lagrangian based model for one such mechanism - a two-link mechanism termed a microscallop, moving in a low Reynolds number environment in a non Newtonian fluid. The modelling proceeds through the conventional Lagrangian construction for a two-link mechanism and then goes on to model the external fluid forces using empirically based models for viscosity to complete the dynamic model. The derived model is then simulated for different initial conditions and key parameters of the non Newtonian fluid, and the results are corroborated with a few existing experimental results on a similar mechanism under identical conditions. Lastly, with a view to implementing control algorithms we explore accessibility of the system at certain configurations.

physics.flu-dyn↗