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…
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48 results for “Combinatorial Analysis”
New analysis shows Thompson Sampling can work with greedy approximations in combinatorial bandits.
problem Thompson Sampling's theoretical limits with greedy approximations in combinatorial semi-bandits.
method Study with greedy oracle, providing lower and upper bounds on regret.
result First theoretical results showing TS can work with greedy approximations, breaking misconceptions.
Improved statistical efficiency of Thompson Sampling for combinatorial semi-bandits.
problem Efficiency of policies in stochastic combinatorial multi-armed bandits with semi-bandit feedback.
method Analysis of Combinatorial Thompson Sampling (CTS) using Beta and Gaussian priors for mutually independent and multivariate sub-Gaussian outcomes.
result CTS provides an efficient policy with optimal asymptotic regret for both mutually independent and multivariate sub-Gaussian outcomes.
Bayesian optimization adapted for discrete spaces using random mappings.
problem Global optimization of expensive black-box functions with discrete variables.
method Embeds discrete space into a convex polytope, performs optimization in continuous space.
result Method outperforms existing methods in large combinatorial spaces.
A new deep learning framework for topological data.
problem Developing models for data on complex topological domains.
method Introducing combinatorial complexes and developing attention-based CCNNs.
result CCNNs outperform existing models in tasks involving mesh shape analysis and graph learning.
We define Discrete Quasi-Einstein metrics (DQE-metrics) as the critical points of discrete total curvature functional on triangulated 3-manifolds. We study DQE-metrics by introducing some combinatorial curvature flows. We prove that these flows produce solutions which converge to discrete quasi-Einstein metrics when th…
Study improves CTS's approximation regret for combinatorial bandits.
problem Improving CTS's performance on non-exact oracles.
method Develops a new upper bound for CTS under specific conditions.
result First approximation regret upper bound for CTS.
CRB tackles rising rewards in combinatorial online learning.
problem Rising rewards in combinatorial online learning.
method CRB framework and CRUCB algorithm.
result Empirical and theoretical validation of CRUCB's effectiveness.
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…
Deep learning uncovers patterns between knot types.
problem Discovering connections between combinatorial and hyperbolic knot invariants.
method Statistical approach using linear regression and deep learning.
result Revealed empirical connections between knot types.
This paper investigates stochastic and adversarial combinatorial multi-armed bandit problems. In the stochastic setting under semi-bandit feedback, we derive a problem-specific regret lower bound, and discuss its scaling with the dimension of the decision space. We propose ESCB, an algorithm that efficiently exploits t…
New method for mixed-variable GSA improves material design efficiency.
problem Designing materials with both quantitative and qualitative variables.
method Integrates LVGP with Sobol' analysis for mixed-variable GSA.
result Accelerates exploration of novel MOF candidates in combinatorial design spaces.
This paper analyzes arbitrage opportunities in Polymarket's NBA markets.
problem Underexplored market microstructure and high-frequency pricing efficiency in decentralized prediction markets.
method Systematic empirical analysis of algorithmic arbitrage using over 75 million limit order book snapshots.
result Microstructural efficiency is profound, with single-market anomalies rare and combinatorial inefficiencies more frequent.
Unified framework for combinatorial and rounding algorithms in experimental design.
problem Designing and analyzing combinatorial and rounding algorithms for experimental design problems.
method Local search framework for combinatorial algorithms and regret minimization framework for rounding algorithms.
result Unified approach to match and improve all known results in D/A/E-design and obtain new results in unknown settings.
This paper extends combinatorial semi-bandits to graph feedback, improving regret bounds.
problem Adversarial combinatorial semi-bandits with graph feedback.
method Introduced graph feedback in combinatorial semi-bandits, using convexified actions and online stochastic mirror descent.
result Optimal regret scales as , interpolating between full and semi-bandit feedback.
A new algorithm balances exploration and exploitation in online decision-making.
problem Balancing exploration and exploitation in online decision-making.
method Proposed -UCB algorithm incorporating conservative mechanism.
result Proved n-step upper regret bound for two situations.
Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.
problem Adversarial combinatorial bandits with general non-linear reward functions.
method Extending existing work on adversarial linear combinatorial bandits, analyzing minimax optimal regret for polynomial and non-polynomial reward functions.
result Minimax optimal regret bounds for adversarial combinatorial bandits with general non-linear reward functions.
A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of t…
Paper analyzes FTPL's effectiveness in combinatorial semi-bandit problems.
problem Optimizing FTPL policy in combinatorial semi-bandit problems.
method Geometric resampling (GR) and conditional geometric resampling (CGR) for FTPL in semi-bandit setting.
result FTPL achieves optimal regret bounds in both Fréchet and Pareto distributions.
Exact pairwise ranking is achievable but not possible under noisy comparisons.
problem Recovering the exact rank of items from noisy pairwise comparisons.
method Information-theoretic upper and lower bounds using the SST model and combinatorial arguments.
result Sharp information-theoretic bounds match in the parametric limit and outperform previous methods.
A Near-Optimal Change-Detection Based Algorithm for Piecewise-Stationary Combinatorial Semi-Banditscs.LG
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…
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 fractal spaces not quasisymmetric to Loewner spaces discovered.
problem Finding new fractal spaces not quasisymmetric to Loewner spaces.
method Introduced iterated graph systems (IGS) to create new fractal spaces.
result Disproved Kleiner's conjecture about self-similar fractals.
Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methodscs.LG
New framework analyzes effectiveness of neural network-based combinatorial problem solvers.
problem Analyzing neural network-based methods for combinatorial optimization problems.
method Introducing a theoretical framework to assess the effectiveness of solution-samplers using policy-gradient methods.
result Positive theoretical answer to the existence of expressive, tractable, and benign optimization landscapes for combinatorial problems.
We propose a sample-efficient alternative for importance weighting for situations where one only has sample access to the probability distribution that generates the observations. Our new method, called Geometric Resampling (GR), is described and analyzed in the context of online combinatorial optimization under semi-b…
New framework tackles submodular welfare with multi-agent combinatorial bandits.
problem Maximizing total welfare among agents with shared constraints and submodular utilities under bandit feedback.
method Proposes an explore-then-commit strategy with randomized assignments for multi-agent combinatorial bandits.
result Achieves regret, first for partition-based submodular welfare problem under bandit feedback.
Algorithm BGLM-OFU minimizes regret in combinatorial causal bandits with binary models.
problem Minimizing expected regret in combinatorial causal bandits with binary generalized linear models.
method BGLM-OFU algorithm based on maximum likelihood estimation for Markovian BGLMs, and causal inference techniques for linear models with hidden variables.
result Achieves regret for binary generalized linear models.
Novel theory combines combinatorial and topological elements.
problem Understanding combinatorial phenomena at the intersection of topology.
method Synthesizes combinatorial and topological approaches with a new framing concept.
result Framed combinatorial spaces exhibit better behavior than classical spaces.
New GFlowNet training framework using policy gradients for combinatorial object generation.
problem Training efficiency and robustness in GFlowNet models.
method Policy-dependent rewards and coupled training strategy for forward and backward policies.
result Advanced RL perspectives for robust gradient estimation improve GFlowNet performance.
A new method reduces both input and output dimensions for better goal-oriented analysis.
problem Simultaneous reduction of input and output dimensions for more accurate analysis.
method Coupled input-output dimension reduction, optimizing gradient-based bounds.
result Determine most informative sensors and influential parameters efficiently.
The paper introduces combinatorial Calabi flows to find hyperbolic metrics on surfaces with boundary.
problem Finding hyperbolic metrics on surfaces with totally geodesic boundaries of given lengths.
method Introducing combinatorial Calabi flows and proving their long time existence and global convergence.
result Proves the long time existence and global convergence of combinatorial Calabi flow on surfaces with boundary.
This paper tackles combinatorial pure exploration for dueling bandits, aiming to find the best candidate-position match.
problem Finding the best candidate-position match in a dueling bandit setting.
method The paper adapts combinatorial pure exploration for multi-armed bandits to dueling bandits, considering both Borda winner and Condorcet winner cases. It designs PAC and exact algorithms for Borda winner and a fully polynomial time approximation scheme (FPTAS) for Condorcet winner.
result The paper introduces the first algorithm with polynomial running time per round for identifying the Condorcet winner in CPE-DB.
The paper tackles combinatorial pure exploration with various feedback structures and proposes efficient algorithms.
problem Identifying the optimal action in a combinatorial space with limited feedback and nonlinear rewards.
method Designs polynomial-time adaptive algorithms for CPE-BL and CPE-PL, providing sample complexity analyses.
result The proposed algorithms achieve sample complexity close to lower bounds and outperform existing methods.
Parameterized discrete uniformization theorems and curvature flows for polyhedral surfaces, IImath.GT
The paper develops algorithms for finding metrics with prescribed combinatorial curvature on polyhedral surfaces.
problem Finding metrics with prescribed combinatorial curvature on polyhedral surfaces.
method Discrete uniformization theorem, combinatorial α-Yamabe flow, combinatorial α-Calabi flow, edge flipping surgery.
result Longtime existence and convergence of combinatorial α-Yamabe flow and combinatorial α-Calabi flow with surgery.
New algorithm for contextual combinatorial bandits with probabilistic arm triggering.
problem Optimizing decisions in dynamic environments with probabilistic arm availability.
method C^2-UCB-T and VAC^2-UCB algorithms with TPM and VM conditions.
result Achieved improved regret bounds for contextual combinatorial bandits.
The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.
problem Discrete conformal structures on polyhedral surfaces and their rigidity.
method Parameterized combinatorial curvature, combinatorial α-Ricci flow, and flow extension through singularities.
result Existence and convergence of combinatorial α-Ricci flow for solving the Yamabe problem.
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 and on a given 3-manifold , each containing a surface that is either essential or a Heegaard surface. We show how a …
EKM solves the K-medoids problem in polynomial time.
problem The -medoids problem in data analysis.
method EKM is a novel algorithm using transformational programming and combinatorial generation.
result EKM solves the -medoids problem in worst-case $O\left(N^{K+1}
ight)$ time complexity.
Efficiently recovers data corrupted by adversarial noise in structured settings.
problem Recovering clean data points from corrupted Gaussian data with low-rank noise and adversarial coordinate corruptions.
method Developed an efficient algorithm using a combinatorial approach to analyze Basis Pursuit (BP) method.
result Achieved nearly-optimal recovery of data points up to a error bound.
We study the periods mapping from the moduli space of real hyperelliptic curves with marked point on an oriented oval to the euclidean space. The mapping arises in the analysis of Chebyshev construction used in the constrained optimization of the uniform norm of polynomials and rational functions. The decomposition of …
CMOSS algorithm reduces regret in combinatorial semi-bandits with efficient computation.
problem Efficiently solving combinatorial semi-bandit problems with minimal regret.
method CMOSS algorithm achieves optimal regret bounds with minimal computational overhead.
result CMOSS achieves optimal regret bounds with minimal computational overhead.
A new algorithm tackles delayed combinatorial semi-bandit with causal relations.
problem Optimizing decisions in a non-stationary environment with delayed and causally related rewards.
method Formalized as a non-stationary delayed combinatorial semi-bandit problem, the approach models causal relations with a directed graph in a stationary structural equation model. The agent learns these relations from delayed feedback to optimize decisions.
result Proved a regret bound for the proposed algorithm's performance.
Fractional combinatorial flow improves surface conformal structures.
problem Improving discrete conformal structures on surfaces.
method Introducing a fractional combinatorial Calabi flow for discrete conformal structures on surfaces.
result Longtime existence and global convergence of the fractional combinatorial Calabi flow for various surface types.
Unified framework for CO problems using RL, providing optimal solutions and convergence guarantees.
problem Combinatorial optimization problems
method Unified framework of Markov decision processes (MDPs) and value-based reinforcement learning (RL) techniques
result RL techniques converge to approximate solutions with a guarantee on optimality gap
Combinatorial method computes Legendrian knot invariant.
problem Computing the Heegaard Floer contact invariant for Legendrian knots.
method Combining Plamenevskaya's combinatorial description with Heegaard Floer theory.
result Hat version of LOSS invariant can be computed combinatorially.
In this paper we determine a number of meaningful compositions of higher order of a set of functions, which is considered in Malesevic (1998), in implicit and explicit form. Results which are obtained are applied to the vector analysis in order to determine the number of meaningful differential operations of higher ord…
Polynomial-time method solves complex combinatorial semi-bandits.
problem Optimal strategies for combinatorial semi-bandits with uncorrelated Gaussian rewards.
method Proposes a polynomial-time method to solve the Graves-Lai optimization problem for various combinatorial structures.
result First known approach to implement asymptotically optimal algorithms in polynomial time for combinatorial semi-bandits.
New combinatorial structure for hierarchically hyperbolic spaces.
problem Constructing new hierarchically hyperbolic spaces.
method Combinatorial hierarchical hyperbolicity criterion to construct and clarify HHS structures.
result HHSs admit a combinatorial structure, clarifying the application of the combinatorial HHS criterion.