Related papers: Overcoming the Curse of Dimensionality in Reinforc…
We study the representation complexity of model-based and model-free reinforcement learning (RL) in the context of circuit complexity. We prove theoretically that there exists a broad class of MDPs such that their underlying transition and…
We study the $L_{\infty}$-approximation of $d$-variate functions from Hilbert spaces via linear functionals as information. It is a common phenomenon in tractability studies that unweighted problems (with each dimension being equally…
In reward-free reinforcement learning (RL), an agent explores the environment first without any reward information, in order to achieve certain learning goals afterwards for any given reward. In this paper we focus on reward-free RL under…
This paper addresses the problem of learning optimal control policies for systems with uncertain dynamics and high-level control objectives specified as Linear Temporal Logic (LTL) formulas. Uncertainty is considered in the workspace…
Reinforcement Learning (RL) has demonstrated tremendous empirical success across numerous challenging domains. However, we lack a strong theoretical understanding of the statistical complexity of RL in environments with large state spaces,…
Deep reinforcement learning (RL) algorithms have recently achieved remarkable successes in various sequential decision making tasks, leveraging advances in methods for training large deep networks. However, these methods usually require…
We explain how to use Kolmogorov Superposition Theorem (KST) to break the curse of dimensionality when approximating a dense class of multivariate continuous functions. We first show that there is a class of functions called…
We study the problem of Reinforcement Learning (RL) with linear function approximation, i.e. assuming the optimal action-value function is linear in a known $d$-dimensional feature mapping. Unfortunately, however, based on only this…
We propose novel classical and quantum online algorithms for learning finite-horizon and infinite-horizon average-reward Markov Decision Processes (MDPs). Our algorithms are based on a hybrid exploration-generative reinforcement learning…
Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL…
We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL). The proposed distributional dynamic programming algorithms…
Reinforcement Learning (RL) has gained substantial attention across diverse application domains and theoretical investigations. Existing literature on RL theory largely focuses on risk-neutral settings where the decision-maker learns to…
This work advances randomized exploration in reinforcement learning (RL) with function approximation modeled by linear mixture MDPs. We establish the first prior-dependent Bayesian regret bound for RL with function approximation; and refine…
Artificial neural networks (ANNs) have become a very powerful tool in the approximation of high-dimensional functions. Especially, deep ANNs, consisting of a large number of hidden layers, have been very successfully used in a series of…
Interest in reinforcement learning (RL) for large-scale systems, comprising extensive populations of intelligent agents interacting with heterogeneous environments, has surged significantly across diverse scientific domains in recent years.…
Since the 1990s, considerable empirical work has been carried out to train statistical models, such as neural networks (NNs), as learned heuristics for combinatorial optimization (CO) problems. When successful, such an approach eliminates…
Thompson sampling (TS) is one of the most popular exploration techniques in reinforcement learning (RL). However, most TS algorithms with theoretical guarantees are difficult to implement and not generalizable to Deep RL. While the emerging…
In recent work it has been shown that determining a feedforward ReLU neural network to within high uniform accuracy from point samples suffers from the curse of dimensionality in terms of the number of samples needed. As a consequence,…
Recently, it has been proposed in the literature to employ deep neural networks (DNNs) together with stochastic gradient descent methods to approximate solutions of PDEs. There are also a few results in the literature which prove that DNNs…
Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the…