arXiv research

A new method uses heat diffusion to efficiently solve combinatorial optimization problems.

The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have no analogue in the classical knot case. These combinatorial formulae contain additional information about how a subdiagram is embedded in a virtual knot diagram. The additional information comes from the second author's…

This work improves privacy in federated combinatorial bandits by balancing regret and privacy.

Algorithm constructs and classifies weaving diagrams using combinatorial methods.

Using the invariant developed in [6], we differentiate four arrangements with the same combinatorial information but in different deformation classes. From these arrangements, we construct four other arrangements such that there is no orientation-preserving homeomorphism between them. Furthermore, some couples of arran…

Exact pairwise ranking is achievable but not possible under noisy comparisons.

This is a survey article about knot Floer homology. We present three constructions of this invariant: the original one using holomorphic disks, a combinatorial description using grid diagrams, and a combinatorial description in terms of the cube of resolutions. We discuss the geometric information carried by knot Floer…

We study quasi-isometry invariants of Gromov hyperbolic spaces, focussing on the l_p-cohomology and closely related invariants such as the conformal dimension, combinatorial modulus, and the Combinatorial Loewner Property. We give new constructions of continuous l_p-cohomology, thereby obtaining information about the l…

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

Deep RL learns to construct objects from 2D images by avoiding brick overlaps.

The paper introduces submodular information measures for machine learning applications.

We address online combinatorial optimization when the player has a prior over the adversary's sequence of losses. In this framework, Russo and Van Roy proposed an information-theoretic analysis of Thompson Sampling based on the information ratio, resulting in optimal worst-case regret bounds. In this paper we introduce…

New combinatorial approach to Goldman-Turaev Lie bialgebra using cyclic word partitions.

We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons satisfying that the total angles at vertices are at least $2π.$ The combinatorial information of these surfaces is shown to be identified with that of Euclidean polyhedral surfaces with negative combinatorial curvature everywher…

We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, \texttt{GLR-CUCB}, which incorporat…

Greedy MI maximization method outperforms existing approaches in nonlinear models.

Study counterfactuals in combinatorial choice using a representative agent model.

Paper tackles safe combinatorial semi-bandits with risk constraints.

Federated learning for combinatorial multi-agent bandits reduces regret and speeds up with fewer communications.

We address online linear optimization problems when the possible actions of the decision maker are represented by binary vectors. The regret of the decision maker is the difference between her realized loss and the best loss she would have achieved by picking, in hindsight, the best possible action. Our goal is to unde…

We study the topology of moduli spaces of closed linkages in \R^d depending on a length vector \ell\in \R^n. In particular, we use equivariant Morse theory to obtain information on the homology groups of these spaces, which works best for odd d. In the case d=5 we calculate the Poincare polynomial in terms of combinato…

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…

Bayesian Optimization for graph node subset functions.

New algorithm for combinatorial bandit problems reduces regret.

The paper tackles budget allocation for multiple campaigns using a novel combinatorial bandit approach.

Attention weights may not accurately highlight important parts due to combinatorial shortcuts.

This is an expository paper, in which we give a summary of some of the joint work of John Luecke and the author on Dehn surgery. We consider the situation where we have two Dehn fillings $M(α)$ and $M(β)$ on a given 3-manifold $M$, each containing a surface that is either essential or a Heegaard surface. We show how a …

New method quantifies redundant information using information bottleneck.

A notion of up and down Grover walks on simplicial complexes are proposed and their properties are investigated. These are abstract Szegedy walks, which is a special kind of unitary operators on a Hilbert space. The operators introduced in the present paper are usual Grover walks on graphs defined by using combinatoria…

Novel theory combines combinatorial and topological elements.

The paper introduces combinatorial Calabi flows to find hyperbolic metrics on surfaces with boundary.

We describe structure of fans for toric varieties with signature 0.

We present and study a partial-information model of online learning, where a decision maker repeatedly chooses from a finite set of actions, and observes some subset of the associated losses. This naturally models several situations where the losses of different actions are related, and knowing the loss of one action p…

New combinatorial framework for geometric realizations of subword complexes.

Meta-SAGE improves deep RL scalability for CO tasks by adapting pre-trained models to larger-scale problems.

OLPA optimizes online user-centric selection with probing, achieving near-optimal regret bounds.

The paper develops algorithms for finding metrics with prescribed combinatorial curvature on polyhedral surfaces.

We consider combinatorial online learning with subset choices when only relative feedback information from subsets is available, instead of bandit or semi-bandit feedback which is absolute. Specifically, we study two regret minimisation problems over subsets of a finite ground set $[n]$, with subset-wise relative prefe…

The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.

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

Study apple tasting feedback in online binary classification, providing new insights into minimax expected mistakes.

New perspective on Heegaard splittings using square complexes and combinatorial measurements.

For triangulated surfaces, we introduce the combinatorial Calabi flow which is an analogue of smooth Calabi flow. We prove that the solution of combinatorial Calabi flow exists for all time. Moreover, the solution converges if and only if Thurston's circle packing exists. As a consequence, combinatorial Calabi flow pro…

Paper introduces probabilistic approach to CO layers in ML.

We construct an elementary, combinatorial kind of topological quantum field theory, based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of a TQFT defined by Honda--Kazez--Matic. This topological field theory stores inf…

Paper reinterprets majorizing measure theorem in terms of coding theory.

Fractional combinatorial flow improves surface conformal structures.

SBBO optimizes complex spaces using sampling-based models.