Related papers: Agnostic Q-learning with Function Approximation in…

For any real numbers $B \ge 1$ and $\delta \in (0, 1)$ and function $f: [0, B] \rightarrow \mathbb{R}$, let $d_{B; \delta} (f) \in \mathbb{Z}_{> 0}$ denote the minimum degree of a polynomial $p(x)$ satisfying $\sup_{x \in [0, B]} \big| p(x)…

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…

In many real world applications, reinforcement learning agents have to optimize multiple objectives while following certain rules or satisfying a list of constraints. Classical methods based on reward shaping, i.e. a weighted combination of…

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

We study reinforcement learning (RL) for a class of continuous-time linear-quadratic (LQ) control problems for diffusions, where states are scalar-valued and running control rewards are absent but volatilities of the state processes depend…

The ODE method has been a workhorse for algorithm design and analysis since the introduction of the stochastic approximation. It is now understood that convergence theory amounts to establishing robustness of Euler approximations for ODEs,…

We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…

In the "correlated sampling" problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to…

In Reinforcement Learning the Q-learning algorithm provably converges to the optimal solution. However, as others have demonstrated, Q-learning can also overestimate the values and thereby spend too long exploring unhelpful states. Double…

We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube $\{0,1\}^n$. Our main result is the following structural theorem: any submodular function is…

We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves…

In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are…

Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…

We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…

We consider optimal sensor scheduling with unknown communication channel statistics. We formulate two types of scheduling problems with the communication rate being a soft or hard constraint, respectively. We first present some structural…

When function approximation is deployed in reinforcement learning (RL), the same problem may be formulated in different ways, often by treating a pre-processing step as a part of the environment or as part of the agent. As a consequence,…

Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an…

We develop deterministic approximation algorithms for the minimum dominating set problem in the CONGEST model with an almost optimal approximation guarantee. For $\epsilon>1/{\text{{poly}}}\log \Delta$ we obtain two algorithms with…

There are many high dimensional function classes that have fast agnostic learning algorithms when assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be confident that…

We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…