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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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48 results for suboptimality gaps

New study shows exponential lower bound for RL even with constant suboptimality gap.

problem Can RL be sample-efficient with a constant suboptimality gap?
method Analyzes reinforcement learning in the online setting with a linearly realizable optimal Q-function.
result An exponential sample complexity lower bound still holds even with a constant suboptimality gap.

Fine-grained gap-dependent regret bounds for reinforcement learning.

problem Achieving optimal regret bounds for reinforcement learning with suboptimality gaps.
method Developed novel analytical frameworks and refined algorithms for UCB-based and non-UCB-based reinforcement learning.
result Established the first fine-grained gap-dependent regret bounds for both UCB-based and non-UCB-based algorithms.

Study quantile multi-armed bandits for identifying the best arm with a specified quantile level.

problem Identifying the arm with the highest quantile in multi-armed bandits with private rewards.
method Proposed a (non-private) and differentially private successive elimination algorithms for best-arm identification.
result The proposed algorithms are essentially optimal for quantile bandit problems, with finite sample complexity even for distributions with infinite support-size.

Improved reinforcement learning for episodes with varying action sets.

problem Reinforcement learning with context-dependent action sets.
method Extends MVP algorithm to handle adversarial and stochastic contexts.
result Established minimax regret bounds of O(SAH3KlogL)O(\sqrt{SAH^3K\log L}) for adversarial contexts.

Develops a Best-of-Both-Worlds algorithm for linear contextual bandits with Tsallis entropy.

problem Linear contextual bandits with i.i.d. contexts.
method Follow-The-Regularized-Leader (FTRL) with Tsallis entropy.
result Achieves $O\left(\log(T)^{\frac{1+β}{2+β}}T^{\frac{1}{2+β}} ight)$ regret under margin condition.

Privacy-preserving reinforcement learning from human feedback using decoupled reward modeling.

problem Training large language models with sensitive user information while preserving privacy.
method Proposes a privacy-preserving framework that imposes differential privacy on reward learning only.
result Privacy contributes an additional additive term to the suboptimality gap, and the upper bound is rate-optimal up to logarithmic factors.

This paper improves Q-learning bounds using reference-advantage decomposition.

problem Improving Q-learning bounds in MDPs with positive suboptimality gaps.
method Develops a novel error decomposition framework to prove gap-dependent regret bounds.
result Establishes logarithmic gap-dependent regret bounds for Q-learning.

In this paper, we propose several improvements on the block-coordinate Frank-Wolfe (BCFW) algorithm from Lacoste-Julien et al. (2013) recently used to optimize the structured support vector machine (SSVM) objective in the context of structured prediction, though it has wider applications. The key intuition behind our i…

2016-05-30abs ↗pdf ↗

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…

2014-10-03abs ↗pdf ↗

Study best arm identification with contextual info, achieving optimal misidentification probability.

problem Identify the best treatment arm with minimal misidentification probability in a small gap scenario.
method Developed RS-AIPW strategy that matches lower bound of misidentification probability in the small-gap regime.
result RS-AIPW strategy is asymptotically optimal for best arm identification.

Improved online Q-learning for MDPs with concentration bounds.

problem Online Q-learning in infinite-horizon discounted MDPs with sublinear regret for large gaps.
method Smoothed εnε_n-Greedy exploration scheme combining εnε_n-greedy and Boltzmann exploration, analyzed using concentration bounds for contractive Markovian stochastic approximation.
result Near-ildeO(N9/10) ilde{O}(N^{9/10}) regret bound for Smoothed εnε_n-Greedy exploration scheme.

Boltzmann exploration is a classic strategy for sequential decision-making under uncertainty, and is one of the most standard tools in Reinforcement Learning (RL). Despite its widespread use, there is virtually no theoretical understanding about the limitations or the actual benefits of this exploration scheme. Does it…

2017-05-29abs ↗pdf ↗

Unified framework for corruption-robust linear bandits with optimal gap-dependent misspecification bounds.

problem Effective learning in linear bandits with corrupted rewards across different corruption models.
method Unified framework for analyzing strong and weak corruption, connection to gap-dependent misspecification, and specialized algorithm.
result Optimal bounds for gap-dependent misspecification in linear bandits.

New algorithm optimizes multi-armed bandit performance in stochastic and adversarial settings.

problem Optimizing multi-armed bandit performance in both stochastic and adversarial environments.
method Follow-the-regularized-leader method with adaptive learning rates.
result First BOBW algorithm with gap-variance-dependent regret bounds in adversarial settings.

AdMRL improves meta-reinforcement learning by minimizing worst-case sub-optimality gap.

problem Meta-reinforcement learning's sensitivity to task distribution shift.
method Model-based adversarial approach with minimax objective and alternating optimization.
result Efficacy in worst-case performance, generalization to out-of-distribution tasks, and sample efficiency.

Policy gradients methods apply to complex, poorly understood, control problems by performing stochastic gradient descent over a parameterized class of polices. Unfortunately, even for simple control problems solvable by standard dynamic programming techniques, policy gradient algorithms face non-convex optimization pro…

2019-06-05abs ↗pdf ↗

Novel IRL method identifies suboptimal medical decisions in ICU data.

problem Identifying suboptimal medical decisions in clinical settings.
method Incorporates Inverse Reinforcement Learning with a pruning step to identify and remove suboptimal actions.
result Pruning step effectively identifies clinical priorities and values from suboptimal data.

This paper closes the gap on matching pursuit's convergence rate.

problem Improving the understanding of matching pursuit's convergence rate.
method Constructing a worst case dictionary to analyze matching pursuit's performance.
result Sharp characterization of matching pursuit's convergence rate as nαn^{-α}, with α0.182α \approx 0.182.

We propose a faster and more accurate method for learning classification trees.

problem Learning optimal binary classification trees is challenging and slow.
method We introduce a stronger MIP formulation and Benders' decomposition method.
result Our method is 50 times faster and improves out-of-sample performance.

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the tensor. We show that this approach can be substantially suboptimal: reliably recov…

2013-07-22abs ↗pdf ↗

Algorithm reduces regret in multi-player bandits with unknown collision rewards.

problem Reducing regret in multi-player multi-armed bandits with unknown collision rewards.
method Proposes an algorithm that combines a modified successive elimination strategy with a communication protocol to estimate suboptimality gaps and coordinate among players.
result Achieves logarithmic regret for the problem when collision reward is unknown.

We introduce a novel theoretical framework for Return On Investment (ROI) maximization in repeated decision-making. Our setting is motivated by the use case of companies that regularly receive proposals for technological innovations and want to quickly decide whether they are worth implementing. We design an algorithm …

2019-05-28abs ↗pdf ↗

New suboptimal algorithm for best subset selection in high-dimensional data.

problem Nonconvex and computationally challenging best subset selection in linear regression.
method Introducing a new suboptimal algorithm and comparing it with other popular methods.
result The new procedure is a competitive suboptimal algorithm for high-dimensional data.

Optimistic covariance-adaptive algorithms improve combinatorial semi-bandits regret.

problem Optimal regret in stochastic combinatorial semi-bandits with adaptive covariance estimation.
method Design of OLS-UCB-C and COS-V algorithms leveraging online covariance estimation.
result Improved gap-free regret with T^1/2 complexity for COS-V.

The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is suboptimal, as it does not attempt to model the entire global signal in any mean…

2017-02-11abs ↗pdf ↗

We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our…

2016-12-16abs ↗pdf ↗

New method for semiparametric bandits reduces regret to optimal levels.

problem Complex reward structures in semiparametric bandits.
method Experimental-design approach with sharp regret bound and PAC bound.
result Minimax regret of ildeO(dT) ilde{O}(\sqrt{dT}) and logarithmic regret under positive suboptimality gap.

The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP conver…

2011-05-05abs ↗pdf ↗

New research shows Byzantine failures hurt generalization more than data poisoning in robust distributed learning.

problem Generalization in robust distributed learning algorithms under Byzantine failures vs. data poisoning.
method Algorithmic stability analysis of robust distributed learning algorithms.
result Byzantine failures yield strictly worse generalization rates than data poisoning.

The paper introduces a new measure of robustness for partially identifiable risks.

problem Achieving robustness when the robust risk is only partially identified.
method Introduces the worst-case robust risk and evaluates existing methods.
result Existing robustness methods are suboptimal in the partially identifiable case.

Proves minimax sample complexity for turn-based stochastic games.

problem Proving theoretical guarantees for reinforcement learning in turn-based stochastic games.
method Developing absorbing TBSG and reward perturbation techniques to handle statistical dependence.
result Empirical Nash equilibrium strategy approximates true Nash equilibrium in turn-based stochastic games.

Develops anytime-valid stopping rules for SGD based on observed trajectory.

problem Stopping stochastic gradient descent (SGD) based on observed trajectory.
method Develops anytime-valid confidence sequences for stochastic gradient methods.
result Statistically valid, time-uniform stopping rules for SGD across convex and nonconvex settings.