Related papers: Multi-Bellman operator for convergence of $Q$-lear…
Value function learning plays a central role in many state-of-the-art reinforcement-learning algorithms. Many popular algorithms like Q-learning do not optimize any objective function, but are fixed-point iterations of some variant of…
Temporal-difference and Q-learning play a key role in deep reinforcement learning, where they are empowered by expressive nonlinear function approximators such as neural networks. At the core of their empirical successes is the learned…
The $Q$-learning algorithm is a simple and widely-used stochastic approximation scheme for reinforcement learning, but the basic protocol can exhibit instability in conjunction with function approximation. Such instability can be observed…
In the reinforcement learning literature, strong theoretical guarantees have been obtained for algorithms applicable to LTI systems. However, in the nonlinear case only weaker results have been obtained for algorithms that mostly rely on…
A primary requirement for any reinforcement learning method is that it should produce policies that improve upon the initial guess. In this work, we show that the widely used Deep Q-Network (DQN) fails to satisfy this minimal criterion --…
This paper discusses a new approach to the fundamental problem of learning optimal Q-functions. In this approach, optimal Q-functions are formulated as saddle points of a nonlinear Lagrangian function derived from the classic Bellman…
This paper develops an inverse reinforcement learning algorithm aimed at recovering a reward function from the observed actions of an agent. We introduce a strategy to flexibly handle different types of actions with two approximations of…
Q-learning is one of the most popular methods in Reinforcement Learning (RL). Transfer Learning aims to utilize the learned knowledge from source tasks to help new tasks to improve the sample complexity of the new tasks. Considering that…
For continuous action spaces, actor-critic methods are widely used in online reinforcement learning (RL). However, unlike RL algorithms for discrete actions, which generally model the optimal value function using the Bellman optimality…
Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure.…
In reinforcement learning (RL), Q-learning is a fundamental algorithm whose convergence is guaranteed in the tabular setting. However, this convergence guarantee does not hold under linear function approximation. To overcome this…
This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of…
We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate $O(1/T)$ and $O(\frac{1}{\log…
Q-functions are widely used in discrete-time learning and control to model future costs arising from a given control policy, when the initial state and input are given. Although some of their properties are understood, Q-functions…
This paper develops a switching-system interpretation of Q-learning with linear function approximation (LFA) based on the joint spectral radius (JSR). We derive an exact linear switched model for the mean dynamics and relate convergence to…
Soft Q-learning is a variation of Q-learning designed to solve entropy regularized Markov decision problems where an agent aims to maximize the entropy regularized value function. Despite its empirical success, there have been limited…
We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this…
The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…
In recent years there has been a collective research effort to find new formulations of reinforcement learning that are simultaneously more efficient and more amenable to analysis. This paper concerns one approach that builds on the linear…