arXiv research

Corrected proof for C^2UCB contextual combinatorial bandit's regret bound.

The paper aims to develop new combinatorial dimensions for bounded memory learning.

New lower bounds for combinatorial multi-armed bandits for general reward functions.

We prove that the number of combinatorially distinct causal 3-dimensional triangulations homeomorphic to the 3-dimensional sphere is bounded by an exponential function of the number of tetrahedra. It is also proven that the number of combinatorially distinct causal 4-dimensional triangulations homeomorphic to the 4-sph…

The paper extends log-Sobolev inequalities to matrix-valued settings using combinatorial methods.

CRB tackles rising rewards in combinatorial online learning.

Optimizes bounds for multiple T-singularities on surfaces.

In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.

New algorithm detects changes in combinatorial semi-bandit rewards.

In this paper we provide a new Bennequin-type inequality for the Rasmussen- Beliakova-Wehrli invariant, featuring the numerical transverse braid invariants (the c-invariants) introduced by the author. From the Bennequin type-inequality, and a combinatorial bound on the value of the c-invariants, we deduce a new computa…

New algorithms tackle adversarial combinatorial bandits with switching costs.

A new algorithm balances exploration and exploitation in online decision-making.

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global structure of the underlying graph. Examples include testing the graph connectivity…

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

The traditional Riemann Mapping Theorem can be proved with circle packing techniques. We prove the Combinatorial Riemann Mapping Theorem for tilings of bounded size using circle packings.

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

The paper classifies compact hyperbolic Coxeter polytopes and improves upper bounds.

A new online learning problem, CAB, tackles matching platforms to maximize user satisfaction.

Paper addresses privacy in combinatorial semi-bandits with improved bounds.

We study combinatorial multi-armed bandit with probabilistically triggered arms (CMAB-T) and semi-bandit feedback. We resolve a serious issue in the prior CMAB-T studies where the regret bounds contain a possibly exponentially large factor of $1/p^*$, where $p^*$ is the minimum positive probability that an arm is trigg…

Bounded-type 3-manifolds arise as combinatorially bounded gluings of irreducible 3-manifolds chosen from a finite list. We prove effective hyperbolization and effective rigidity for a broad class of 3-manifolds of bounded type and large gluing heights. Specifically, we show the existence and uniqueness of hyperbolic me…

Improved regret bounds for Thompson Sampling in combinatorial settings.

For triangulated surfaces locally embedded in the standard hyperbolic space, we introduce combinatorial Calabi flow as the negative gradient flow of combinatorial Calabi energy. We prove that the flow produces solutions which converge to ZCCP-metric (zero curvature circle packing metric) if the initial energy is small …

We analyze the regret of combinatorial Thompson sampling (CTS) for the combinatorial multi-armed bandit with probabilistically triggered arms under the semi-bandit feedback setting. We assume that the learner has access to an exact optimization oracle but does not know the expected base arm outcomes beforehand. When th…

New bounds on query learning complexity for various concept classes.

In this paper, we give the sharp upper bound for the number of vertices with positive curvature in a planar graph with nonnegative combinatorial curvature. Based on this, we show that the automorphism group of a planar---possibly infinite---graph with nonnegative combinatorial curvature and positive total curvature is …

We construct combinatorial volume forms of hyperbolic three manifolds fibering over the circle. These forms define non-trivial classes in bounded cohomology. After introducing a new seminorm on exact bounded cohomology, we use these combinatorial classes to show that, in degree 3, the zero norm subspace of the bounded …

Study on combinatorial Yamabe flow on hyperbolic surfaces, proving existence and uniqueness.

New method improves solving combinatorial optimization problems with smoothed policies.

This paper extends combinatorial semi-bandits to graph feedback, improving regret bounds.

A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we close the problem of computationally and sample effi…

RNNs learn combinatorial graph problems with sample complexity bounds.

In this paper, we study the combinatorial multi-armed bandit problem (CMAB) with probabilistically triggered arms (PTAs). Under the assumption that the arm triggering probabilities (ATPs) are positive for all arms, we prove that a class of upper confidence bound (UCB) policies, named Combinatorial UCB with exploration …

A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-s…

Transformers capture combinatorial tasks with bounded error and logarithmic sample dependence.

Efficient algorithms exploit structure of uncertainty for combinatorial semi-bandits.

Improved regret bounds for contextual combinatorial semi-bandits with linear payoffs.

We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. A focus is given to dimension 3 where slicings are normal surfaces. In the case of 2-neighborly 3-manifolds and quadrangulated slicings, a lower bound on the number of quadrilaterals of normal surfaces depending on the …

Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.

A matroid is a notion of independence in combinatorial optimization which is closely related to computational efficiency. In particular, it is well known that the maximum of a constrained modular function can be found greedily if and only if the constraints are associated with a matroid. In this paper, we bring togethe…

Study proves hyperbolic structures for link complements in Seifert fibered spaces.

Paper analyzes FTPL's effectiveness in combinatorial semi-bandit problems.

We study how the length and the twisting parameter of a curve change along a Teichmuller geodesic. We then use our results to provide a formula for the Teichmuller distance between two hyperbolic metrics on a surface, in terms of the combinatorial complexity of curves of bounded lengths in these two metrics.

Study adapts combinatorial semi-bandit for piecewise stationary, causally related rewards.

Study of combinatorial Yamabe flows in 3D spaces.

New method uses diffusion models for unsupervised combinatorial optimization.

In a recent work [2] with Datta, we introduced the mu vector (with respect to a given field) of simplicial complexes and used it to study tightness and lower bounds. In this paper, we modify the definition of mu vectors. With the new definition, most results of [2] become correct without the hypothesis of 2-neighbourli…

Algorithm improves movie recommendation efficiency with fairness constraints.