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Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications. Previous primal-dual style approaches suffer from instability issues and lack optimality…
Continued demand for accurate and computationally efficient transport methods to solve optically thick, fixed-source transport problems has inspired research on variance-reduction (VR) techniques for Monte Carlo (MC). Methods that use…
We study distributed multiagent optimization over (directed, time-varying) graphs. We consider the minimization of $F+G$ subject to convex constraints, where $F$ is the smooth strongly convex sum of the agent's losses and $G$ is a nonsmooth…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
The autonomous systems need to decide how to react to the changes at runtime efficiently. The ability to rigorously analyze the environment and the system together is theoretically possible by the model-driven approaches; however, the model…
Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
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…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
We tackle the issue of finding a good policy when the number of policy updates is limited. This is done by approximating the expected policy reward as a sequence of concave lower bounds which can be efficiently maximized, drastically…
Policy optimization methods with function approximation are widely used in multi-agent reinforcement learning. However, it remains elusive how to design such algorithms with statistical guarantees. Leveraging a multi-agent performance…
We consider the traffic control problem of dynamic routing over parallel servers, which arises in a variety of engineering systems such as transportation and data transmission. We propose a semi-gradient, on-policy algorithm that learns an…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
We propose policy gradient algorithms which learn risk-sensitive policies in a reinforcement learning (RL) framework. Our proposed algorithms maximize the distortion risk measure (DRM) of the cumulative reward in an episodic Markov decision…
We study policy optimization algorithms for computing correlated equilibria in multi-player general-sum Markov Games. Previous results achieve $O(T^{-1/2})$ convergence rate to a correlated equilibrium and an accelerated $O(T^{-3/4})$…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…
We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and…
In this paper we propose several novel distributed gradient-based temporal difference algorithms for multi-agent off-policy learning of linear approximation of the value function in Markov decision processes with strict information…
We present a preconditioned Monte Carlo method for computing high-dimensional multivariate normal and Student-$t$ probabilities arising in spatial statistics. The approach combines a tile-low-rank representation of covariance matrices with…