Study on identifying the best decision with continuous, separable rewards in stochastic multi-armed bandit.
problem Identifying the best decision with continuous, separable rewards in stochastic multi-armed bandit.
method Proposed an adaptive learning algorithm for CPE-CS problem, analyzed sample complexity with new hardness measure.
result Upper and lower bounds of sample complexity for CPE-CS problem.
This paper tackles combinatorial optimization under uncertainty with limited feedback.
problem Tackling combinatorial optimization problems with uncertain or unknown parameters.
method Review of techniques for combinatorial pure exploration with limited bandit feedback.
result Introduction of methods for combinatorial optimization under uncertainty with limited observation.
New algorithm identifies optimal actions in large reward spaces efficiently.
problem Finding the best action from a large set of options with minimal trials.
method GenTS-Explore algorithm for real-valued combinatorial pure exploration.
result Achieves optimal sample complexity for large action sets.
New algorithms improve hiring decisions by optimizing tiered interview processes.
problem Optimizing tiered interview allocation for better hiring decisions.
method Casted tiered hiring as a combinatorial pure exploration (CPE) problem in the stochastic multi-armed bandit setting, presenting new algorithms in PAC and fixed-budget settings.
result Our algorithms select a near-optimal cohort with provable guarantees, making better hiring decisions or using less budget than the status quo.
Polynomial-time algorithms for identifying the best super arm in full-bandit feedback.
problem Finding the best super arm in a set of single arms with full-bandit feedback.
method Proposed polynomial-time bandit algorithms and an approximation algorithm for the 0-1 quadratic maximization problem.
result Polynomial-time algorithms for top-k selection problems.
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…
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.
New algorithm finds high-reward combinatorial sets with fewest pulls.
problem Finding high-reward combinatorial sets with unknown individual arm rewards.
method Successive acceptance and elimination based on combinatorial structure.
result Algorithm requires minimal combinatorial oracle calls, making it practical for large problems.
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.
We study the combinatorial pure exploration problem Best-Set in stochastic multi-armed bandits. In a Best-Set instance, we are given n n n arms with unknown reward distributions, as well as a family F \mathcal{F} F of feasible subsets over the arms. Our goal is to identify the feasible subset in F \mathcal{F} F with the maxi…
New algorithms find the best subset of distributions with minimal samples.
problem Finding the best subset of distributions with minimal samples.
method Design of new algorithms for combinatorial pure exploration in multi-arm bandit framework.
result Achieve new sample-complexity bounds with polynomial improvements.
The study analyzes batched methods for early stopping in stochastic multi-armed bandits.
problem Early stopping in stochastic multi-armed bandits with fixed confidence.
method Instance-dependent lower bounds and a general batched algorithm with upper bounds.
result Upper and lower bounds on the number of batches and sample complexity.
New experimental design minimizes regret in bandits.
problem Minimizing regret in online stochastic linear and combinatorial bandits.
method Experimental design-based algorithm balancing information gain and reward.
result State-of-the-art finite time regret guarantees and computational efficiency.
Algorithm identifies best arm in combinatorial bandits with semi-bandit feedback.
problem Identifying the best arm in combinatorial bandits with semi-bandit feedback.
method Interpreted as a sequential zero-sum game, developed a CombGame meta-algorithm with finite time guarantees.
result First computationally efficient algorithm that is asymptotically optimal and has competitive empirical performance.
Paper explores algebraic, topological, and combinatorial properties of singular virtual braids.
problem Understanding singular virtual braids and their properties.
method Algebraic relations, topological and combinatorial bijections, presentations.
result A bijection between singular abstract braids and singular virtual braids, leading to a presentation of the singular pure virtual braid monoid.
New algorithms solve games to find optimal exploration strategies.
problem Sequentially gather information to answer queries about stochastic environments.
method Interpret optimisation problem as a game and use iterative strategies to estimate its saddle point.
result First finite confidence guarantees for pure exploration in exponential families.
Study on sample complexity for pure exploration in feedback graph settings.
problem Sample complexity of pure exploration in online learning with feedback graphs.
method Derive instance-specific lower bounds and present asymptotically optimal algorithm TaS-FG.
result TaS-FG is asymptotically optimal and efficient across different graph configurations.
Optimizes pure exploration in linear bandits with a new algorithm.
problem Best-arm identification in linear stochastic bandits.
method Developed the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits.
result Avoids the pitfall of a simple but difficult instance and bypasses the need to solve an optimal design problem.
This paper explores how boolean formulas can be learned by deep neural networks.
problem Understanding the learnability of boolean formulas by deep neural networks.
method Analysis of boolean formulas associated with model-sampling benchmarks, combinatorial optimization problems, and random 3-CNFs.
result Neural networks outperform rule-based systems and pure symbolic approaches in learning boolean formulas.
New algorithm for combinatorial bandit problems reduces regret.
problem Optimal selection of sets of arms in bandit problems.
method SGB algorithm with optimized exploration of unselected arms.
result Achieves ( 1 − 1 / e ) (1-1/e) ( 1 − 1/ e ) -regret bound of O ( n 1 3 k 2 3 T 2 3 log ( T ) 2 3 ) \mathcal{O}(n^{\frac{1}{3}} k^{\frac{2}{3}} T^{\frac{2}{3}} \log(T)^{\frac{2}{3}}) O ( n 3 1 k 3 2 T 3 2 log ( T ) 3 2 ) . Pure combinatorial models for BPL_n and Gauss map of a combinatorial manifold are described.
New algorithms find all ε-good arms in stochastic bandits.
problem Finding all arms with means above a specified threshold in stochastic bandits.
method Two algorithms introduced to identify all ε-good arms.
result Demonstrated great empirical performance on large datasets.
New method classifies spinor orbits in dimensions up to 14.
problem Classify orbits of the spin group in semi-spinor spaces.
method Use pure spinors and combinatorial constraints to classify orbits.
result Classification of spinor orbits in dimensions up to 14.
Combinatorial proof shows knot invariant in Lipshitz's grid homology.
problem Proving knot invariance in Lipshitz's grid homology.
method Purely combinatorial proof.
result Proves 'minus' version of Lipshitz's double-point enhanced grid homology is a knot invariant.
New algorithms learn best actions without taking bad ones in combinatorial problems.
problem Learning best actions without taking bad ones in combinatorial problems.
method Formalized as stochastic combinatorial semi-bandits with exchangeable actions, designed efficient learning algorithms, bounded n-step regret.
result Real-world experiments show algorithms can learn without violating strict constraints.
Efficiently clusters noisy data with minimal queries.
problem Clustering elements with noisy oracle feedback.
method Combination of sampling strategy and correlation clustering algorithm.
result First polynomial-time algorithms for NP-hard optimization problem.
KG-A2C agent learns natural language IF games by reasoning and constraining action spaces.
problem Challenges of natural language understanding, partial observability, and combinatorially large action spaces in IF games.
method Builds a dynamic knowledge graph while exploring, constraining actions using templates.
result Outperforms current IF agents across various games with larger action spaces.
Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.
problem Identifying the best arm in stochastic linear bandits with fixed confidence.
method Extending an algorithm designed for Best Arm Identification to the ε ε ε -Thresholding Bandit Problem (TBP). result Asymptotically optimal algorithm for TBP.
Algorithm balances online and offline data for linear bandits.
problem Online learning with an offline dataset in linear bandits.
method Proposes a linear bandit algorithm that uses offline data early and increasingly favors exploration as the horizon grows.
result Establishes regret bounds showing competitive performance with both purely online and offline solutions.
Combinatorial proof of grid homology properties.
problem Properties of double-point enhanced grid homology.
method Purely combinatorial proof, extended to Z \mathbb{Z} Z coefficients. result Skein exact sequence obeyed by grid homology.
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.
New algorithm reduces exploration in structured stochastic bandits.
problem Wide class of stochastic bandit problems with known structural properties.
method Developed OSSB algorithm that matches minimal exploration rates of sub-optimal arms.
result OSSB's regret matches asymptotic instance-specific regret lower bound.
Optimizes matching in weighted graphs with semi-bandit sampling.
problem Finding optimal pairings in weighted graphs with sequential sampling.
method Leverages rank-1 assumption on adjacency matrix to reduce sample complexity and regret.
result Achieves linear dependency in the number of vertices for sample complexity and regret.
The paper tackles pure exploration in multi-armed bandits with low rank structure using oblivious sampling.
problem Pure exploration in multi-armed bandits with low rank reward sequences.
method The approach involves separating the exploration strategy from feedback, using oblivious sampling, and incorporating kernel information of reward vectors.
result Efficient algorithms with regret bound O ( d ( ln N ) / n ) O(d\sqrt{(\ln N)/n}) O ( d ( ln N ) / n ) for both time-varying and fixed cases, with a lower bound gap of O ( ln N ) O(\sqrt{\ln N}) O ( ln N ) . This work introduces CAET, an algorithm for cost-aware pairwise pure exploration.
problem Identifying optimal arm pairs with varying costs in multi-armed bandits.
method Introduces a framework for pairwise pure exploration with arm-specific costs, derives a lower bound, and proposes CAET algorithm.
result CAET optimizes cumulative cost and approaches the lower bound asymptotically.
Improved Boltzmann exploration reduces regret in stochastic MAB problems.
problem Improving regret in stochastic multi-armed bandit problems.
method A modified Boltzmann exploration with a doubling trick.
result Achieves O ( K log 1 + α T ) O(K\log^{1+α} T) O ( K log 1 + α T ) regret, improving on previous results. The paper offers efficient algorithms for combinatorial and linear bandits using empirical process theory.
problem Optimal algorithms for combinatorial and linear bandits with practical sample complexity.
method Empirical process theory, Gaussian-width, minimizing experimental design objective.
result Sample complexity matches lower bounds, especially for combinatorial classes.
Develops a combinatorial semi-bandit method for electric vehicle charging station selection.
problem Long-distance navigation for BEVs with unknown charging station availability and performance.
method Combinatorial semi-bandit framework, pre-processing road network, Bayesian modeling, Thompson Sampling, BayesUCB, Epsilon-greedy.
result Demonstrates improved navigation performance on long-distance BEV charging station selection.
CORe uses randomization to explore bandit problems without external noise.
problem Exploration in stochastic bandit problems.
method Randomizes past observations to exploit variance in rewards.
result Achieves i l d e O ( d n log K ) ilde O(d\sqrt{n\log K}) i l d e O ( d n log K ) regret bound in stochastic linear bandits. 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.
This paper explores Brunnian twin groups and their properties.
problem Alexander-Markov correspondence for isotopy classes of immersed circles.
method Diagrammatic representations and combinatorial structures.
result Brunnian twin groups are free groups when more than two strands are involved.
Unified algorithm for efficient pure exploration using dual variables.
problem Efficiently achieving a specific goal through adaptive experimentation.
method Introducing dual variables to derive optimal allocation conditions, leading to Information-Directed Selection.
result Top-two Thompson sampling attains asymptotic optimality for Gaussian best-arm identification.
Regularization-induced exploration improves contextual bandit performance.
problem Complex reward models in real-world contextual bandits are hard to explore effectively.
method Regularization-induced exploration using stochasticity in cross-validation.
result Regularization-induced exploration leads to reliable exploration in large-scale business environments.
Study inert and ambiguous classes in modular group using combinatorial methods.
problem Counting inert and ambiguous conjugacy classes in modular group.
method Purely combinatorial approach using word length in free product representation.
result Exact counting formulas and asymptotic growth rates for inert and ambiguous classes.
New algorithm finds optimal sample complexity for pure exploration with multiple good answers.
problem Determining the optimal number of samples needed to explore multiple good answers in a bandit problem.
method Derive lower bound using game equilibrium, extend Track-and-Stop algorithm to multiple answers.
result New algorithm has asymptotic sample complexity matching the derived lower bound.
Develops first optimal algorithm for logistic bandits.
problem Pure exploration in logistic bandits.
method Logistic track-and-stop (Log-TS) algorithm.
result Asymptotically matches lower bound for expected sample complexity.
Study explores properties of bipartite knots.
problem None explicitly stated; focuses on properties of bipartite knots.
method Exploration of combinatorial structure.
result Rich combinatorial structure of bipartite knots.