arXiv research

We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the actio…

Efficient algorithms for planning in cooperative multi-agent reinforcement learning with combinatorial action spaces.

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 …

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

A framework for reinforcement learning tackles CVRP with competitive results.

Paper tackles combinatorial reinforcement learning with preference feedback.

Math verifies Aganagic's proposal for Khovanov homology.

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

We give a complete classification of irreducible symmetric spaces for which there exist proper SL(2,R)-actions as isometries, using the criterion for proper actions by T. Kobayashi [Math. Ann. '89] and combinatorial techniques of nilpotent orbits. In particular, we classify irreducible symmetric spaces that admit surfa…

The paper studies quaternionic structures on GKM graphs and their relation to torus actions on quaternionic projective spaces.

Let X=G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial formulas for this action when X is an irreducible hermitian symmetric space of compact …

In complex tasks, such as those with large combinatorial action spaces, random exploration may be too inefficient to achieve meaningful learning progress. In this work, we use a curriculum of progressively growing action spaces to accelerate learning. We assume the environment is out of our control, but that the agent …

Introduces Conditional Action Trees to simplify RL action spaces.

The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of simplicial and cubical subdivisions of manifolds and, especially, spheres. We describe…

This paper has been withdrawn by the author. Improved versions (arXiv:1109.5548 and arXiv:0708.4190) are accepted.

New method for evaluating and learning in complex decision-making scenarios.

New algorithm identifies optimal actions in large reward spaces efficiently.

Simplifies large action space bandits by selecting representative actions.

We consider the problem of online combinatorial optimization under semi-bandit feedback, where a learner has to repeatedly pick actions from a combinatorial decision set in order to minimize the total losses associated with its decisions. After making each decision, the learner observes the losses associated with its a…

Solves action selection for large spaces in RL, achieving near-optimal performance.

New method reduces bias and variance in OPE for large action spaces.

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

In many practical problems, a learning agent may want to learn the best action in hindsight without ever taking a bad action, which is significantly worse than the default production action. In general, this is impossible because the agent has to explore unknown actions, some of which can be bad, to learn better action…

Study boundary actions on CAT(0) spaces, proving topological freeness.

SRL embeds combinatorial optimization into RL for better decision-making.

We give examples of symplectic actions of a cyclic group, inducing a trivial action on homology, on four-manifolds that admit Hamiltonian circle actions, and show that they do not extend to Hamiltonian circle actions. Our work applies holomorphic methods to extend combinatorial tools developed for circle actions to stu…

A small cover was introduced by Davis and Januszkiewicz as an $n$-dimensional closed manifold with a locally standard $Z_2)^n$-action such that its orbit space is a simple convex polytope. There exist a one-to-one correspondence between small covers and $(Z_2)^n$-colored polytopes. In this paper we study a construction…

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

This paper contains some more results on the topology of a nondegenerate action of $\mathbb{R}^n$ on a compact connected $n$-manifold $M$ when the action is totally hyperbolic (i.e. its toric degree is zero). We study the $\mathbb{R}$-action generated by a fixed vector of $\mathbb{R}^n$, that provides some results on t…

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)xU(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds.

We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of act…

Algorithm optimizes bandit decisions with changing action sets using Gaussian processes.

We make a few observations on the absence of geometric and topological rigidity for acylindrically hyperbolic and relatively hyperbolic groups. In particular, we demonstrate the lack of a well-defined limit set for acylindrical actions on hyperbolic spaces, even under the assumption of universality. We also prove a sta…

A new method learns action representations for reinforcement learning.

A transitive smooth action of a connected Lie group G on a manifold M is called almost primitive (resp. primitive) if G doesn't contain any proper subgroup (resp. any proper normal subgroup) whose induced action on M is transitive as well. The aim of the present work is to investigate some combinatory properties of sym…

The paper develops quaternionic toric geometry and classifies local actions.

moment maps arise as a generalization of genuine moment maps on symplectic manifolds when the symplectic structure is discarded, but the relation between the mapping and the action is kept. Particular examples of abstract moment maps had been used in Hamiltonian mechanics for some time, but the abstract notion originat…

In sponsored search, keyword recommendations help advertisers to achieve much better performance within limited budget. Many works have been done to mine numerous candidate keywords from search logs or landing pages. However, the strategy to select from given candidates remains to be improved. The existing relevance-ba…

New method minimizes decision errors in large treatment spaces.

Deep RL improves Diplomacy performance, outperforming previous methods.

The action of the mapping class group of a surface on the collection of homotopy classes of disjointly embedded curves or arcs in the surface is discussed here as a tool for understanding Riemann's moduli space and its topological and geometric invariants. Furthermore, appropriate completions, elaborations, or quotient…

We consider the Markov Decision Process (MDP) of selecting a subset of items at each step, termed the Select-MDP (S-MDP). The large state and action spaces of S-MDPs make them intractable to solve with typical reinforcement learning (RL) algorithms especially when the number of items is huge. In this paper, we present …

We give a proof, using harmonic maps from disks to real trees, of Skora's theorem (Morgan-Otal (1993), Skora (1990), originally conjectured by Shalen): if G is the fundamental group of a surface of genus at least 2, then any small minimal G-action on a real tree is dual to the lift of a measured foliation. Analytic too…

Portfolio traders strive to identify dynamic portfolio allocation schemes so that their total budgets are efficiently allocated through the investment horizon. This study proposes a novel portfolio trading strategy in which an intelligent agent is trained to identify an optimal trading action by using deep Q-learning. …

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…

One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional faces are diffeomorphic. It follows that two simple convex polytop…

Improved statistical efficiency of Thompson Sampling for combinatorial semi-bandits.

New combinatorial structure for hierarchically hyperbolic spaces.