arXiv subjects

Shalabh Bhatnagar

Publications and source records attributed to Shalabh Bhatnagar.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Scheduling for Remote State Estimation over Hybrid Channels

We study optimal scheduling for remote state estimation over a network with two heterogeneous communication channels: a fast but unreliable channel and a slow but reliable channel. To capture temporal correlations in packet losses, we model the unreliable channel as a Gilbert-Elliott (GE) channel. The remote estimation setup consists of a source, a sensor, and a remote estimator. The source evolves as a discrete-time autoregressive (AR) process, and the sensor decides at each time whether to use the fast unreliable channel or the slow reliable channel. We formulate the scheduling problem faced by the sensor as a Markov decision process (MDP) with a continuous state-space and consider minimizing the infinite horizon average cost criterion, where the cost consists of the squared estimation error and the transmission energy consumed. We establish the existence of an optimal stationary policy. We then characterize the structure of an optimal policy, and show that it has a threshold structure with respect to the estimation error. An optimal policy chooses from amongst the two channels based on whether the error exceeds certain thresholds, where the threshold value depends upon the GE channel state. When the system parameters are unknown, we propose an actor-critic (AC) learning algorithm that exploits the threshold structure of an optimal policy. Numerical results demonstrate that the proposed AC algorithm learns the policy structure effectively and achieves performance close to that of the optimal policy computed using the relative value iteration (RVI).

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arXiv2026

Stochastic Mirror Descent under Iterate-Dependent Markov Noise: Analysis in the Asymptotic and Finite Time Regimes

We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems with decision-dependent uncertainty; however, they introduce bias and temporal dependence, which render standard techniques developed for i.i.d.\ noise inapplicable. In this work, we analyze the stochastic mirror descent algorithm under iterate-dependent Markov noise. We first establish almost sure convergence for both convex and non-convex problems under the mild assumption of Lipschitz continuity of the objective function, without requiring differentiability. We then derive finite-time concentration bounds for smooth objectives. In the convex setting, the resulting sample complexity matches the classical rate of stochastic mirror descent under i.i.d.\ noise. In the non-convex setting, we obtain a sample complexity bound in terms of the norm of the Riemannian gradient over the probability simplex. Overall, our results establish a unified convergence framework for stochastic mirror descent with state-dependent Markov noise, and highlight its behavior in both convex and non-convex regimes.

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arXiv2026

Policy Gradient Methods for Non-Markovian Reinforcement Learning

We study policy gradient methods for reinforcement learning in non-Markovian decision processes (NMDPs), where observations and rewards depend on the entire interaction history. To handle this dependence, the agent maintains an internal state that is recursively updated to provide a compact summary of past observations and actions. In contrast to approaches that treat the agent state dynamics as fixed or learn it via predictive objectives, we propose a reward-centric formulation that jointly optimizes the agent state dynamics and the control policy to maximize the expected cumulative reward. To this end, we consider a class of Agent State-Markov (ASM) policies, comprising an agent state dynamics and a control policy that maps the agent state to actions. We establish a novel policy gradient theorem for ASM policies, extending the classical policy gradient results from the Markovian setting to episodic and infinite-horizon discounted NMDPs. Building on this gradient expression, we propose the Agent State-Markov Policy Gradient (ASMPG) algorithm, which leverages the recursive structure of the agent state dynamics for efficient optimization. We establish finite-time and almost sure convergence guarantees, and empirically demonstrate that, on a range of non-Markovian tasks, ASMPG outperforms baselines that learn state representations via predictive objectives.

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arXiv2026

Finite-time analysis of Multi-timescale Stochastic Optimization Algorithms

We present a finite-time analysis of two smoothed functional stochastic approximation algorithms for simulation-based optimization. The first is a two time-scale gradient-based method, while the second is a three time-scale Newton-based algorithm that estimates both the gradient and the Hessian of the objective function $J$. Both algorithms involve zeroth order estimates for the gradient/Hessian. Although the asymptotic convergence of these algorithms has been established in prior work, finite-time guarantees of two-timescale stochastic optimization algorithms in zeroth order settings have not been provided previously. For our Newton algorithm, we derive mean-squared error bounds for the Hessian estimator and establish a finite-time bound on $\min\limits_{0 \le m \le T} \mathbb{E}\| \nabla J(\theta(m)) \|^2$, showing convergence to first-order stationary points. The analysis explicitly characterizes the interaction between multiple time-scales and the propagation of estimation errors. We further identify step-size choices that balance dominant error terms and achieve near-optimal convergence rates. We also provide corresponding finite-time guarantees for the gradient algorithm under the same framework. The theoretical results are further validated through experiments on the Continuous Mountain Car environment.

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arXiv2026

High-Probability Bounds for SGD under the Polyak-Lojasiewicz Condition with Markovian Noise

We present the first uniform-in-time high-probability bound for SGD under the PL condition, where the gradient noise contains both Markovian and martingale difference components. This significantly broadens the scope of finite-time guarantees, as the PL condition arises in many machine learning and deep learning models while Markovian noise naturally arises in decentralized optimization and online system identification problems. We further allow the magnitude of noise to grow with the function value, enabling the analysis of many practical sampling strategies. In addition to the high-probability guarantee, we establish a matching $1/k$ decay rate for the expected suboptimality. Our proof technique relies on the Poisson equation to handle the Markovian noise and a probabilistic induction argument to address the lack of almost-sure bounds on the objective. Finally, we demonstrate the applicability of our framework by analyzing three practical optimization problems: token-based decentralized linear regression, supervised learning with subsampling for privacy amplification, and online system identification.

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arXiv2026

Generalized Random Direction Newton Algorithms for Stochastic Optimization

We present a family of generalized Hessian estimators of the objective using random direction stochastic approximation (RDSA) by utilizing only noisy function measurements. The form of each estimator and the order of the bias depend on the number of function measurements. In particular, we demonstrate that estimators with more function measurements exhibit lower-order estimation bias. We show the asymptotic unbiasedness of the estimators. We also perform asymptotic and non-asymptotic convergence analyses for stochastic Newton methods that incorporate our generalized Hessian estimators. Finally, we perform numerical experiments to validate our theoretical findings.

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arXiv2025

Jointly Optimal Policies for Remote Estimation of Autoregressive Markov Processes over Time-Correlated Fading Channel

We study a remote estimation setup with an autoregressive (AR) Markov process, a sensor, and a remote estimator. The sensor observes the process and sends encoded observations to the estimator as packets over an unreliable communication channel modeled as the Gilbert-Elliot (GE) channel. We assume that the sensor gets to observe the channel state by the ACK/NACK feedback mechanism only when it attempts a transmission while it does not observe the channel state when no transmission attempt is made. The objective is to design a transmission scheduling strategy for the sensor, and an estimation strategy for the estimator that are jointly optimal, i.e., they minimize the expected value of an infinite-horizon cumulative discounted cost defined as the sum of squared estimation error over time and the sensor's transmission power. Since the sensor and the estimator have access to different information sets, this constitutes a decentralized stochastic control problem. We formulate this problem as a partially observed Markov decision process (POMDP) and show the existence of jointly optimal transmission and estimation strategies that have a simple structure. More specifically, an optimal transmission strategy exhibits a threshold structure, i.e., the sensor attempts a transmission only when its belief about the channel being in a good state exceeds a threshold that depends on a certain error. Moreover, an optimal estimation strategy follows a `Kalman-like' update rule. When the channel parameters are unknown, we exploit this structure to design an actor-critic reinforcement learning algorithm that converges to a locally optimal policy. Simulations show the learned policy performs close to a globally optimal one, with about a 5.5% average relative gap across evaluated parameters.

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arXiv2025

Deep SOR Minimax Q-learning for Two-player Zero-sum Game

In this work, we consider the problem of a two-player zero-sum game. In the literature, the successive over-relaxation Q-learning algorithm has been developed and implemented, and it is seen to result in a lower contraction factor for the associated Q-Bellman operator resulting in a faster value iteration-based procedure. However, this has been presented only for the tabular case and not for the setting with function approximation that typically caters to real-world high-dimensional state-action spaces. Furthermore, such settings in the case of two-player zero-sum games have not been considered. We thus propose a deep successive over-relaxation minimax Q-learning algorithm that incorporates deep neural networks as function approximators and is suitable for high-dimensional spaces. We prove the finite-time convergence of the proposed algorithm. Through numerical experiments, we show the effectiveness of the proposed method over the existing Q-learning algorithm. Our ablation studies demonstrate the effect of different values of the crucial successive over-relaxation parameter.

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arXiv2025

Enabling Off-Policy Imitation Learning with Deep Actor Critic Stabilization

Learning complex policies with Reinforcement Learning (RL) is often hindered by instability and slow convergence, a problem exacerbated by the difficulty of reward engineering. Imitation Learning (IL) from expert demonstrations bypasses this reliance on rewards. However, state-of-the-art IL methods, exemplified by Generative Adversarial Imitation Learning (GAIL)Ho et. al, suffer from severe sample inefficiency. This is a direct consequence of their foundational on-policy algorithms, such as TRPO Schulman et.al. In this work, we introduce an adversarial imitation learning algorithm that incorporates off-policy learning to improve sample efficiency. By combining an off-policy framework with auxiliary techniques specifically, in this case a double Q network based stabilization and value learning without reward function inference we demonstrate a reduction in the samples required to robustly match expert behavior.

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arXiv2025

Convergence of Multiagent Learning Systems for Traffic control

Rapid urbanization in cities like Bangalore has led to severe traffic congestion, making efficient Traffic Signal Control (TSC) essential. Multi-Agent Reinforcement Learning (MARL), often modeling each traffic signal as an independent agent using Q-learning, has emerged as a promising strategy to reduce average commuter delays. While prior work Prashant L A et. al has empirically demonstrated the effectiveness of this approach, a rigorous theoretical analysis of its stability and convergence properties in the context of traffic control has not been explored. This paper bridges that gap by focusing squarely on the theoretical basis of this multi-agent algorithm. We investigate the convergence problem inherent in using independent learners for the cooperative TSC task. Utilizing stochastic approximation methods, we formally analyze the learning dynamics. The primary contribution of this work is the proof that the specific multi-agent reinforcement learning algorithm for traffic control is proven to converge under the given conditions extending it from single agent convergence proofs for asynchronous value iteration.

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arXiv2025

Finite Time Analysis of Constrained Natural Critic-Actor Algorithm with Improved Sample Complexity

Recent studies have increasingly focused on non-asymptotic convergence analyses for actor-critic (AC) algorithms. One such effort introduced a two-timescale critic-actor algorithm for the discounted cost setting using a tabular representation, where the usual roles of the actor and critic are reversed. However, only asymptotic convergence was established there. Subsequently, both asymptotic and non-asymptotic analyses of the critic-actor algorithm with linear function approximation were conducted. In our work, we introduce the first natural critic-actor algorithm with function approximation for the long-run average cost setting and under inequality constraints. We provide the non-asymptotic convergence guarantees for this algorithm. Our analysis establishes optimal learning rates and we also propose a modification to enhance sample complexity. We further show the results of experiments on three different Safety-Gym environments where our algorithm is found to be competitive in comparison with other well known algorithms.

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arXiv2025

Convergent Reinforcement Learning Algorithms for Stochastic Shortest Path Problem

In this paper we propose two algorithms in the tabular setting and an algorithm for the function approximation setting for the Stochastic Shortest Path (SSP) problem. SSP problems form an important class of problems in Reinforcement Learning (RL), as other types of cost-criteria in RL can be formulated in the setting of SSP. We show asymptotic almost-sure convergence for all our algorithms. We observe superior performance of our tabular algorithms compared to other well-known convergent RL algorithms. We further observe reliable performance of our function approximation algorithm compared to other algorithms in the function approximation setting.

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arXiv2025

Zeroth-Order Non-smooth Non-convex Optimization via Gaussian Smoothing

This paper addresses stochastic optimization of Lipschitz-continuous, nonsmooth and nonconvex objectives over compact convex sets, where only noisy function evaluations are available. While gradient-free methods have been developed for smooth nonconvex problems, extending these techniques to the nonsmooth setting remains challenging. The primary difficulty arises from the absence of a Taylor series expansion for Clarke subdifferentials, which limits the ability to approximate and analyze the behavior of the objective function in a neighborhood of a point. We propose a two time-scale zeroth-order projected stochastic subgradient method leveraging Gaussian smoothing to approximate Clarke subdifferentials. First, we establish that the expectation of the Gaussian-smoothed subgradient lies within an explicitly bounded error of the Clarke subdifferential, a result that extends prior analyses beyond convex/smooth settings. Second, we design a novel algorithm with coupled updates: a fast timescale tracks the subgradient approximation, while a slow timescale drives convergence. Using continuous-time dynamical systems theory and robust perturbation analysis, we prove that iterates converge almost surely to a neighborhood of the set of Clarke stationary points, with neighborhood size controlled by the smoothing parameter. To our knowledge, this is the first zeroth-order method achieving almost sure convergence for constrained nonsmooth nonconvex optimization problems.

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arXiv2025

An Actor-Critic Algorithm with Function Approximation for Risk Sensitive Cost Markov Decision Processes

In this paper, we consider the risk-sensitive cost criterion with exponentiated costs for Markov decision processes and develop a model-free policy gradient algorithm in this setting. Unlike additive cost criteria such as average or discounted cost, the risk-sensitive cost criterion is less studied due to the complexity resulting from the multiplicative structure of the resulting Bellman equation. We develop an actor-critic algorithm with function approximation in this setting and provide its asymptotic convergence analysis. We also show the results of numerical experiments that demonstrate the superiority in performance of our algorithm over other recent algorithms in the literature.

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arXiv2025

Accelerating SfM-based Pose Estimation with Dominating Set

This paper introduces a preprocessing technique to speed up Structure-from-Motion (SfM) based pose estimation, which is critical for real-time applications like augmented reality (AR), virtual reality (VR), and robotics. Our method leverages the concept of a dominating set from graph theory to preprocess SfM models, significantly enhancing the speed of the pose estimation process without losing significant accuracy. Using the OnePose dataset, we evaluated our method across various SfM-based pose estimation techniques. The results demonstrate substantial improvements in processing speed, ranging from 1.5 to 14.48 times, and a reduction in reference images and point cloud size by factors of 17-23 and 2.27-4, respectively. This work offers a promising solution for efficient and accurate 3D pose estimation, balancing speed and accuracy in real-time applications.

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arXiv2025

A policy gradient approach for Finite Horizon Constrained Markov Decision Processes

The infinite horizon setting is widely adopted for problems of reinforcement learning (RL). These invariably result in stationary policies that are optimal. In many situations, finite horizon control problems are of interest and for such problems, the optimal policies are time-varying in general. Another setting that has become popular in recent times is of Constrained Reinforcement Learning, where the agent maximizes its rewards while it also aims to satisfy some given constraint criteria. However, this setting has only been studied in the context of infinite horizon MDPs where stationary policies are optimal. We present an algorithm for constrained RL in the Finite Horizon Setting where the horizon terminates after a fixed (finite) time. We use function approximation in our algorithm which is essential when the state and action spaces are large or continuous and use the policy gradient method to find the optimal policy. The optimal policy that we obtain depends on the stage and so is non-stationary in general. To the best of our knowledge, our paper presents the first policy gradient algorithm for the finite horizon setting with constraints. We show the convergence of our algorithm to a constrained optimal policy. We also compare and analyze the performance of our algorithm through experiments and show that our algorithm performs better than some other well known algorithms.

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arXiv2024

Gradient-Weighted Feature Back-Projection: A Fast Alternative to Feature Distillation in 3D Gaussian Splatting

We introduce a training-free method for feature field rendering in Gaussian splatting. Our approach back-projects 2D features into pre-trained 3D Gaussians, using a weighted sum based on each Gaussian's influence in the final rendering. While most training-based feature field rendering methods excel at 2D segmentation but perform poorly at 3D segmentation without post-processing, our method achieves high-quality results in both 2D and 3D segmentation. Experimental results demonstrate that our approach is fast, scalable, and offers performance comparable to training-based methods.

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arXiv2024

Gradient-Driven 3D Segmentation and Affordance Transfer in Gaussian Splatting Using 2D Masks

3D Gaussian Splatting has emerged as a powerful 3D scene representation technique, capturing fine details with high efficiency. In this paper, we introduce a novel voting-based method that extends 2D segmentation models to 3D Gaussian splats. Our approach leverages masked gradients, where gradients are filtered by input 2D masks, and these gradients are used as votes to achieve accurate segmentation. As a byproduct, we discovered that inference-time gradients can also be used to prune Gaussians, resulting in up to 21% compression. Additionally, we explore few-shot affordance transfer, allowing annotations from 2D images to be effectively transferred onto 3D Gaussian splats. The robust yet straightforward mathematical formulation underlying this approach makes it a highly effective tool for numerous downstream applications, such as augmented reality (AR), object editing, and robotics. The project code and additional resources are available at https://jojijoseph.github.io/3dgs-segmentation.

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