Related papers: Span-Agnostic Optimal Sample Complexity and Oracle…

In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm,…

We study the online estimation of the optimal policy of a Markov decision process (MDP). We propose a class of Stochastic Primal-Dual (SPD) methods which exploit the inherent minimax duality of Bellman equations. The SPD methods update a…

Much of modern learning theory has been split between two regimes: the classical offline setting, where data arrive independently, and the online setting, where data arrive adversarially. While the former model is often both computationally…

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…

The Robust Markov Decision Process (RMDP) framework focuses on designing control policies that are robust against the parameter uncertainties due to the mismatches between the simulator model and real-world settings. An RMDP problem is…

We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a…

We consider minimization of composite functions of the form $f(g(x))+h(x)$, where $f$ and $h$ are convex functions (which can be nonsmooth) and $g$ is a smooth vector mapping. In addition, we assume that $g$ is the average of finite number…

We introduce a financial portfolio optimization framework that allows us to automatically select the relevant assets and estimate their weights by relying on a sorted $\ell_1$-Norm penalization, henceforth SLOPE. Our approach is able to…

In this paper, we study meta learning for support (i.e., the set of non-zero entries) recovery in high-dimensional precision matrix estimation where we reduce the sufficient sample complexity in a novel task with the information learned…

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

We study the problem of policy evaluation with linear function approximation and present efficient and practical algorithms that come with strong optimality guarantees. We begin by proving lower bounds that establish baselines on both the…

We present a novel data-driven strategy to choose the hyperparameter $k$ in the $k$-NN regression estimator without using any hold-out data. We treat the problem of choosing the hyperparameter as an iterative procedure (over $k$) and…

We propose dynamic sampled stochastic approximation (SA) methods for stochastic optimization with a heavy-tailed distribution (with finite 2nd moment). The objective is the sum of a smooth convex function with a convex regularizer.…

Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…

Policy gradient methods are widely used in reinforcement learning. Yet, the nonconvexity of policy optimization poses significant challenges in understanding the global convergence of policy gradient methods. For a class of finite-horizon…

We investigate the problems of model estimation and reward-free learning in episodic Block MDPs. In these MDPs, the decision maker has access to rich observations or contexts generated from a small number of latent states. We are first…

We study reinforcement learning in non-episodic factored Markov decision processes (FMDPs). We propose two near-optimal and oracle-efficient algorithms for FMDPs. Assuming oracle access to an FMDP planner, they enjoy a Bayesian and a…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

We study the minimax sample complexity of $\varepsilon$-best arm identification in linear bandits. Given a compact action set $\mathcal{X}$ that spans $\mathbb{R}^d$ and an unknown reward vector $\theta\in\mathbb{R}^d$, the goal is to…