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We present the first finite-sample analysis of policy evaluation in robust average-reward Markov Decision Processes (MDPs). Prior work in this setting have established only asymptotic convergence guarantees, leaving open the question of…
Model predictive control (MPC) is a popular control method that has proved effective for robotics, among other fields. MPC performs re-planning at every time step. Re-planning is done with a limited horizon per computational and real-time…
Applying the max-product (and belief-propagation) algorithms to loopy graphs is now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there…
We propose a stochastic model predictive control (MPC) framework for linear systems subject to joint-in-time chance constraints under unknown disturbance distributions. Unlike existing approaches that rely on parametric or Gaussian…
Many safety-critical real-time systems operate under harsh environment and are subject to soft errors caused by transient or intermittent faults. It is critical and yet often very challenging to apply fault tolerance techniques in these…
An increasing number of applications are exploiting sampling-based algorithms for planning, optimization, and inference. The Markov Chain Monte Carlo (MCMC) algorithms form the computational backbone of this emerging branch of machine…
Partially observable Markov decision processes (POMDPs) is a rich mathematical framework that embraces a large class of complex sequential decision-making problems under uncertainty with limited observations. However, the complexity of…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
We study the computational limits of Low-Rank Adaptation (LoRA) for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient…
The formal verification and controller synthesis for Markov decision processes that evolve over uncountable state spaces are computationally hard and thus generally rely on the use of approximations. In this work, we consider the…
The practicality of reinforcement learning algorithms has been limited due to poor scaling with respect to the problem size, as the sample complexity of learning an $\epsilon$-optimal policy is $\tilde{\Omega}\left(|S||A|H^3 /…
"Weakly coupled dynamic program" describes a broad class of stochastic optimization problems in which multiple controlled stochastic processes evolve independently but subject to a set of linking constraints imposed on the controls. One…
This paper proposes a novel robust Model Predictive Control (MPC) scheme for linear discrete-time systems affected by model uncertainty described by interval matrices. The key feature of the proposed method is a bound on the uncertainty…
The core of the Model Predictive Control (MPC) method in every step of the algorithm consists in solving a time-dependent optimization problem on the prediction horizon of the MPC algorithm, and then to apply a portion of the optimal…
This paper studies function approximation for finite horizon discrete time Markov decision processes under certain convexity assumptions. Uniform convergence of these approximations on compact sets is proved under several sampling schemes…
The Weighted Tree Augmentation Problem (WTAP) is a fundamental well-studied problem in the field of network design. Given an undirected tree $G=(V,E)$, an additional set of edges $L \subseteq V\times V$ disjoint from $E$ called…
Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the flow of information. Natural approaches are convergence of…
We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk…
Integrated task and motion planning has emerged as a challenging problem in sequential decision making, where a robot needs to compute high-level strategy and low-level motion plans for solving complex tasks. While high-level strategies…
We study multi-robot persistent monitoring on weighted graphs, where node weights encode monitoring priorities and edge weights encode travel distances. The goal is to design joint robot trajectories that minimize the worst-case weighted…