Research

Near Optimal Exploration-Exploitation in Non-Communicating Markov Decision Processes

December 3, 2018

Abstract

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This results in weakly-communicating or multi-chain MDPs. In this paper, we introduce TUCRL, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with SC communicating states, A actions and ΓCSC possible communicating next states, we derive a Õ(DC √ ΓCSCAT) regret bound, where DC is the diameter (i.e., the length of the longest shortest path between any two states) of the communicating part of the MDP. This is in contrast with existing optimistic algorithms (e.g., UCRL, Optimistic PSRL) that suffer linear regret in weakly-communicating MDPs, as well as posterior sampling or regularised algorithms (e.g., REGAL), which require prior knowledge on the bias span of the optimal policy to achieve sub-linear regret. We also prove that in weakly-communicating MDPs, no algorithm can ever achieve a logarithmic growth of the regret without first suffering a linear regret for a number of steps that is exponential in the parameters of the MDP. Finally, we report numerical simulations supporting our theoretical findings and showing how TUCRL overcomes the limitations of the state-of-the-art.

Download the Paper

Related Publications

November 27, 2022

Core Machine Learning

Neural Attentive Circuits

Nicolas Ballas, Bernhard Schölkopf, Chris Pal, Francesco Locatello, Li Erran, Martin Weiss, Nasim Rahaman, Yoshua Bengio

November 27, 2022

November 27, 2022

Near Instance-Optimal PAC Reinforcement Learning for Deterministic MDPs

Andrea Tirinzoni, Aymen Al Marjani, Emilie Kaufmann

November 27, 2022

November 16, 2022

NLP

Memorization Without Overfitting: Analyzing the Training Dynamics of Large Language Models

Kushal Tirumala, Aram H. Markosyan, Armen Aghajanyan, Luke Zettlemoyer

November 16, 2022

November 10, 2022

Computer Vision

Learning State-Aware Visual Representations from Audible Interactions

Unnat Jain, Abhinav Gupta, Himangi Mittal, Pedro Morgado

November 10, 2022

April 08, 2021

Responsible AI

Integrity

Towards measuring fairness in AI: the Casual Conversations dataset

Caner Hazirbas, Joanna Bitton, Brian Dolhansky, Jacqueline Pan, Albert Gordo, Cristian Canton Ferrer

April 08, 2021

April 30, 2018

The Role of Minimal Complexity Functions in Unsupervised Learning of Semantic Mappings | Facebook AI Research

Tomer Galanti, Lior Wolf, Sagie Benaim

April 30, 2018

April 30, 2018

Computer Vision

NAM – Unsupervised Cross-Domain Image Mapping without Cycles or GANs | Facebook AI Research

Yedid Hoshen, Lior Wolf

April 30, 2018

December 11, 2019

Speech & Audio

Computer Vision

Hyper-Graph-Network Decoders for Block Codes | Facebook AI Research

Eliya Nachmani, Lior Wolf

December 11, 2019

Help Us Pioneer The Future of AI

We share our open source frameworks, tools, libraries, and models for everything from research exploration to large-scale production deployment.