Related papers: The Sample Complexity of Approximate Rejection Sam…

Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $\ell_1$ distance essentially at most a constant times…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…

We consider the optimal sample complexity theory of tabular reinforcement learning (RL) for maximizing the infinite horizon discounted reward in a Markov decision process (MDP). Optimal worst-case complexity results have been developed for…

Deep neural network training spends most of the computation on examples that are properly handled, and could be ignored. We propose to mitigate this phenomenon with a principled importance sampling scheme that focuses computation on…

We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…

We present an algorithm based on posterior sampling (aka Thompson sampling) that achieves near-optimal worst-case regret bounds when the underlying Markov Decision Process (MDP) is communicating with a finite, though unknown, diameter. Our…

The current paper studies the problem of agnostic $Q$-learning with function approximation in deterministic systems where the optimal $Q$-function is approximable by a function in the class $\mathcal{F}$ with approximation error $\delta \ge…

We study fast rates of convergence in the setting of nonparametric online regression, namely where regret is defined with respect to an arbitrary function class which has bounded complexity. Our contributions are two-fold: - In the…

We develop a new analysis of sampling-based motion planning in Euclidean space with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli (2011) and subsequent work. Particularly, we prove…

Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…

We consider the problem of approximating and learning disjunctions (or equivalently, conjunctions) on symmetric distributions over $\{0,1\}^n$. Symmetric distributions are distributions whose PDF is invariant under any permutation of the…

Finding a small spectral approximation for a tall $n \times d$ matrix $A$ is a fundamental numerical primitive. For a number of reasons, one often seeks an approximation whose rows are sampled from those of $A$. Row sampling improves…

We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…

We present a reduction from reinforcement learning (RL) to no-regret online learning based on the saddle-point formulation of RL, by which "any" online algorithm with sublinear regret can generate policies with provable performance…

We revisit the fundamental problem of learning with distribution shift, in which a learner is given labeled samples from training distribution $D$, unlabeled samples from test distribution $D'$ and is asked to output a classifier with low…

We consider a reinforcement learning setting in which the deployment environment is different from the training environment. Applying a robust Markov decision processes formulation, we extend the distributionally robust $Q$-learning…

Rejection sampling is a common tool for low dimensional problems ($d \leq 2$), often touted as an "easy" way to obtain valid samples from a distribution $f(\cdot)$ of interest. In practice it is non-trivial to apply, often requiring…

Consider an open set $\mathbb{D}\subseteq\mathbb{R}^n$, equipped with a probability measure $\mu$. An important characteristic of a smooth function $f:\mathbb{D}\rightarrow\mathbb{R}$ is its \emph{second-moment matrix} $\Sigma_{\mu}:=\int…

Uniformity testing is arguably one of the most fundamental distribution testing problems. Given sample access to an unknown distribution $\mathbf{p}$ on $[n]$, one must decide if $\mathbf{p}$ is uniform or $\varepsilon$-far from uniform (in…