Related papers: Reward Redistribution for CVaR MDPs using a Bellma…

In many sequential decision-making problems one is interested in minimizing an expected cumulative cost while taking into account \emph{risk}, i.e., increased awareness of events of small probability and high consequences. Accordingly, the…

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance $\tau$. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is…

Distributional reinforcement learning (DRL) studies the evolution of full return distributions under Bellman updates rather than focusing on expected values. A classical result is that the distributional Bellman operator is contractive…

We consider an online stochastic game with risk-averse agents whose goal is to learn optimal decisions that minimize the risk of incurring significantly high costs. Specifically, we use the Conditional Value at Risk (CVaR) as a risk measure…

We study whether a risk-sensitive objective from asset-pricing theory -- recursive utility -- improves reinforcement learning for portfolio allocation. The Bellman equation under recursive utility involves a certainty equivalent (CE) of…

Exploration is a crucial and distinctive aspect of reinforcement learning (RL) that remains a fundamental open problem. Several methods have been proposed to tackle this challenge. Commonly used methods inject random noise directly into the…

We consider the stochastic shortest path planning problem in MDPs, i.e., the problem of designing policies that ensure reaching a goal state from a given initial state with minimum accrued cost. In order to account for rare but important…

A Markov decision process can be parameterized by a transition kernel and a reward function. Both play essential roles in the study of reinforcement learning as evidenced by their presence in the Bellman equations. In our inquiry of various…

Control Barrier functions (CBFs) have attracted extensive attention for designing safe controllers for their deployment in real-world safety-critical systems. However, the perception of the surrounding environment is often subject to…

It was recently shown that dynamic programming (DP) methods for finding static CVaR-optimal policies in Markov Decision Processes (MDPs) can fail when based on the dual formulation, yet the root cause of this failure remains unclear. We…

We consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes…

The interaction between an artificial agent and its environment is bi-directional. The agent extracts relevant information from the environment, and affects the environment by its actions in return to accumulate high expected reward.…

Conditional value-at-risk (CoVaR) is one of the most important measures of systemic risk. It is defined as the high quantile conditional on a related variable being extreme, widely used in the field of quantitative risk management. In this…

We study value-iteration (VI) algorithms for solving general (a.k.a. multichain) Markov decision processes (MDPs) under the average-reward criterion, a fundamental but theoretically challenging setting. Beyond the difficulties inherent to…

Safe navigation is a fundamental challenge in multi-robot systems due to the uncertainty surrounding the future trajectory of the robots that act as obstacles for each other. In this work, we propose a principled data-driven approach where…

Reinforcement learning (RL) with continuous time and state/action spaces is often data-intensive and brittle under nuisance variability and shift, motivating methods that exploit value-preserving structures to stabilize and improve…

We propose a novel distributionally robust $Q$-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The…

Finding optimal policies which maximize long term rewards of Markov Decision Processes requires the use of dynamic programming and backward induction to solve the Bellman optimality equation. However, many real-world problems require…

Existing reinforcement learning (RL) methods struggle with complex dynamical systems that demand interactions at high frequencies or irregular time intervals. Continuous-time RL (CTRL) has emerged as a promising alternative by replacing…

In this paper, we consider the stochastic iterative counterpart of the value iteration scheme wherein only noisy and possibly biased approximations of the Bellman operator are available. We call this counterpart as the approximate value…