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The continuous nature of belief states in POMDPs presents significant computational challenges in learning the optimal policy. In this paper, we consider an approach that solves a Partially Observable Reinforcement Learning (PORL) problem…

In Multi-Input Multi-Output (MIMO) systems, Maximum-Likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a…

Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm,…

We investigate the local linear convergence properties of the Alternating Direction Method of Multipliers (ADMM) when applied to Semidefinite Programming (SDP). A longstanding belief suggests that ADMM is only capable of solving SDPs to…

In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…

Learning and optimal control under robust Markov decision processes (MDPs) have received increasing attention, yet most existing theory, algorithms, and applications focus on finite-horizon or discounted models. Long-run average-reward…

This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating…

We study the sequential decision making problem of maximizing the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon…

Since the 1960s I proposed that we could understand and replicate the highest level of intelligence seen in the brain, by building ever more capable and general systems for adaptive dynamic programming (ADP), which is like reinforcement…

For infinite-horizon average-cost criterion problems, there exist relatively few rigorous approximation and reinforcement learning results. In this paper, for Markov Decision Processes (MDPs) with standard Borel spaces, (i) we first provide…

We consider the infinite-horizon linear Markov Decision Processes (MDPs), where the transition probabilities of the dynamic model can be linearly parameterized with the help of a predefined low-dimensional feature mapping. While the…

There is a growing interest in using electric vehicles (EVs) and drones for many applications. However, battery-oriented issues, including range anxiety and battery degradation, impede adoption. Battery swap stations are one alternative to…

We formally verify executable algorithms for solving Markov decision processes (MDPs) in the interactive theorem prover Isabelle/HOL. We build on existing formalizations of probability theory to analyze the expected total reward criterion…

Enforcing state and input constraints during reinforcement learning (RL) in continuous state spaces is an open but crucial problem which remains a roadblock to using RL in safety-critical applications. This paper leverages invariant sets to…

Recent advances have significantly improved our understanding of the sample complexity of learning in average-reward Markov decision processes (AMDPs) under the generative model. However, much less is known about the constrained…

This paper considers the problem of finding near-optimal Markovian randomized (MR) policies for finite-state-action, infinite-horizon, constrained risk-sensitive Markov decision processes (CRSMDPs). Constraints are in the form of standard…

We consider the problem of learning an $\varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Given access to a generative model, we achieve rate-optimal sample…

On-demand ride-pooling (e.g., UberPool) has recently become popular because of its ability to lower costs for passengers while simultaneously increasing revenue for drivers and aggregation companies. Unlike in Taxi on Demand (ToD) services…