arXiv research

This paper tackles combinatorial optimization under uncertainty with limited feedback.

This paper tackles combinatorial pure exploration for dueling bandits, aiming to find the best candidate-position match.

New algorithm finds high-reward combinatorial sets with fewest pulls.

The paper tackles combinatorial pure exploration with various feedback structures and proposes efficient algorithms.

We study the Combinatorial Pure Exploration problem with Continuous and Separable reward functions (CPE-CS) in the stochastic multi-armed bandit setting. In a CPE-CS instance, we are given several stochastic arms with unknown distributions, as well as a collection of possible decisions. Each decision has a reward accor…

New algorithm identifies optimal actions in large reward spaces efficiently.

Algorithm identifies best arm in combinatorial bandits with semi-bandit feedback.

We study a specific \textit{combinatorial pure exploration stochastic bandit problem} where the learner aims at finding the set of arms whose means are above a given threshold, up to a given precision, and \textit{for a fixed time horizon}. We propose a parameter-free algorithm based on an original heuristic, and prove…

We study the combinatorial pure exploration problem Best-Set in stochastic multi-armed bandits. In a Best-Set instance, we are given $n$ arms with unknown reward distributions, as well as a family $\mathcal{F}$ of feasible subsets over the arms. Our goal is to identify the feasible subset in $\mathcal{F}$ with the maxi…

We design new algorithms for the combinatorial pure exploration problem in the multi-arm bandit framework. In this problem, we are given $K$ distributions and a collection of subsets $\mathcal{V} \subset 2^{[K]}$ of these distributions, and we would like to find the subset $v \in \mathcal{V}$ that has largest mean, whi…

This paper explores how boolean formulas can be learned by deep neural networks.

Pure combinatorial models for BPL_n and Gauss map of a combinatorial manifold are described.

Interactive Fiction games are text-based simulations in which an agent interacts with the world purely through natural language. They are ideal environments for studying how to extend reinforcement learning agents to meet the challenges of natural language understanding, partial observability, and action generation in …

New method classifies spinor orbits in dimensions up to 14.

We study the problem of stochastic combinatorial pure exploration (CPE), where an agent sequentially pulls a set of single arms (a.k.a. a super arm) and tries to find the best super arm. Among a variety of problem settings of the CPE, we focus on the full-bandit setting, where we cannot observe the reward of each singl…

Efficiently clusters noisy data with minimal queries.

New experimental design minimizes regret in bandits.

We prove that the "minus" version of Lipshitz's double-point enhanced grid homology is a knot invariant through purely combinatorial means.

Combinatorial proof of grid homology properties.

Goussarov, Polyak, and Viro proved that finite type invariants of knots are ``finitely multi-local'', meaning that on a knot diagram, sums of quantities, defined by local information, determine the value of the knot invariant. The result implies the existence of Gauss diagram combinatorial formulas for finite type inva…

Given an orientable surface with boundary and a free homotopy class, we present a purely combinatorial algorithm which produces a representative of that homotopy class with minimal self intersection.

The paper tackles pure exploration in multi-armed bandits with low rank structure using oblivious sampling.

Optimizes matching in weighted graphs with semi-bandit sampling.

This work introduces CAET, an algorithm for cost-aware pairwise pure exploration.

The paper offers efficient algorithms for combinatorial and linear bandits using empirical process theory.

Study on sample complexity for pure exploration in feedback graph settings.

Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.

Unified algorithm for efficient pure exploration using dual variables.

Given a huge set of applicants, how should a firm allocate sequential resume screenings, phone interviews, and in-person site visits? In a tiered interview process, later stages (e.g., in-person visits) are more informative, but also more expensive than earlier stages (e.g., resume screenings). Using accepted hiring mo…

This paper explores Brunnian twin groups and their properties.

Study inert and ambiguous classes in modular group using combinatorial methods.

Study explores properties of bipartite knots.

Develops first optimal algorithm for logistic bandits.

Optimizes pure exploration in linear bandits with a new algorithm.

In this paper we discuss algebraic, combinatorial and topological properties of singular virtual braids. On the algebraic side we state the relations between classical and virtual singular objects, in addition we discuss a Birman-like conjecture for the virtual case. On the topological and combinatorial side, we prove …

Study pure exploration in high-dimensional feature spaces using adaptive embeddings.

The study analyzes batched methods for early stopping in stochastic multi-armed bandits.

New exploration bonuses improve reinforcement learning efficiency.

We present in this article a family of new combinatorial identities via purely differential/complex geometry methods, which include as a speical case a unified and explicit formula for Chern numbers of all complex flag manifolds. Our strategy is to construct concrete circle actions with isolated fixed points on these m…

It is shown that for any piecewise-linear closed orientable manifold of odd dimension there exists an invariantly defined metric on the determinant line of cohomology with coefficients in an arbitrary flat bundle E over the manifold (E is not required to be unimodular). The construction of this metric (called Poincare …

New algorithm eliminates arms to minimize regret in complex bandit problems.

Proposes qPO, a new acquisition strategy for batched Bayesian optimization that maximizes the probability of including the optimum.

We prove that the complement of any affine 2-arrangement in R^d is minimal, that is, it is homotopy equivalent to a cell complex with as many i-cells as its i-th rational Betti number. For the proof, we provide a Lefschetz-type hyperplane theorem for complements of 2-arrangements, and introduce Alexander duality for co…

Constructs subvarieties in translation surface strata using combinatorial input.

Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplexwise linear embedding of the triangulation into euclidean space is "as convex as possible". It can thus be understood as a generalization of the concept of convexity. In even dimensions, super-neighborliness is known to be …

VCSMC improves efficiency in Bayesian phylogenetic inference.

UCB algorithm adapted for large-scale, non-sub-Gaussian problems.

We give a purely combinatorial construction of colored $\mathfrak{sl}_n$ link homology. The invariant takes values in a 2-category where 2-morphisms are given by foams, singular cobordisms between $\mathfrak{sl}_n$ webs; applying a (TQFT-like) representable functor recovers (colored) Khovanov-Rozansky homology. Novel f…