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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 Sub-optimality Gaps

Algorithm reduces regret in misspecified linear contextual bandits.

problem Misspecified linear contextual bandits with bounded misspecification.
method Data selection scheme for online regression, leveraging uncertainty.
result Regret bound of O~(d2/Δ)\tilde O(d^2/Δ) when ζO~(Δ/d)ζ \leq \tilde O(Δ/\sqrt{d}).

Unified hybrid RL algorithm improves online RL performance with offline data.

problem Improving reinforcement learning performance with limited online data.
method A unified hybrid RL algorithm combining offline and online data.
result Unified algorithm achieves state-of-the-art results in sub-optimality gap and online learning regret.

Paper tackles sample-efficient RL for linearly realizable MDPs with limited revisiting.

problem Sample-efficient reinforcement learning for linearly realizable MDPs with limited revisiting.
method Develops a new sampling protocol that allows for backtracking and revisiting states in a controlled manner.
result Achieves polynomial sample complexity scaling with feature dimension, horizon, and inverse sub-optimality gap.

We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the cost incurred by playing the certainty equivalent controller on the true system …

2019-02-21abs ↗pdf ↗

Logarithmic regret achieved in RL with linear function approximation.

problem Achieving logarithmic regret in reinforcement learning with linear function approximation.
method LSVI-UCB for linear MDP assumption, UCRL-VTR for linear mixture MDP assumption.
result Logarithmic regret bounds established for RL with linear function approximation.

Optimal algorithms identify non-dominated arms in multi-output linear bandit models.

problem Identifying the Pareto Set in multi-output linear bandit models.
method Design-based algorithms for Pareto Set Identification (PSI) in a structured multi-output linear bandit model.
result Nearly optimal guarantees in both fixed-budget and fixed-confidence 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.

This paper tackles robust policy learning under concept drifts, improving upon existing methods.

problem Tackles robust policy learning under concept drifts, improving upon existing methods.
method Develops a doubly-robust estimator and a learning algorithm to maximize policy value within a given policy class.
result The proposed algorithm achieves sub-optimality gap of the order κ(Π)n1/2κ(Π)n^{-1/2}, demonstrating substantial improvement over existing benchmarks.

New model predicts optimal control for restless bandit problems.

problem Optimizing control in restless bandit problems with minimal assumptions.
method Model Predictive Control with rolling horizon linear programming.
result Sub-optimality gap of O(1/√N) under general conditions, and exp(-Ω(N)) under local-stability condition.

In many environments, only a relatively small subset of the complete state space is necessary in order to accomplish a given task. We develop a simple technique using emergency stops (e-stops) to exploit this phenomenon. Using e-stops significantly improves sample complexity by reducing the amount of required explorati…

2019-12-03abs ↗pdf ↗

Previous work on recommender systems mainly focus on fitting the ratings provided by users. However, the response patterns, i.e., some items are rated while others not, are generally ignored. We argue that failing to observe such response patterns can lead to biased parameter estimation and sub-optimal model performanc…

2012-10-16abs ↗pdf ↗

Paper bounds PAC RL sample complexity in deterministic MDPs.

problem Identify ε-optimal policy with high probability.
method Proposes nearly matching upper and lower bounds on sample complexity, introduces deterministic return gap, uses graph-theoretical concepts and maximum-coverage exploration.
result First nearly matching upper and lower bounds on sample complexity for PAC RL in deterministic MDPs.

Optimizes ranking of top-k players from partial comparison data.

problem Identifying the top-k players from incomplete pairwise comparisons.
method Maximum Likelihood Estimator (MLE) and Spectral Method.
result MLE achieves optimal partial and exact recovery, while Spectral Method is sub-optimal.

One of the key approaches to save samples in reinforcement learning (RL) is to use knowledge from an approximate model such as its simulator. However, how much does an approximate model help to learn a near-optimal policy of the true unknown model? Despite numerous empirical studies of transfer reinforcement learning, …

2019-12-06abs ↗pdf ↗

This work develops a unified framework for RLHF with general ff-divergence regularization.

problem Theoretical understanding of general ff-divergence regularization in RLHF.
method Holistic approach across ff-divergence class, two algorithms based on distinct sampling principles.
result Provably efficient algorithms with O(logT)O(\log T) regret and O(1/T)O(1/T) sub-optimality gap.

The paper tackles system identification via Hankel nuclear norm regularization, improving estimation rates and singular value gaps.

problem Identifying low-order linear systems from limited data.
method Hankel nuclear norm regularization to encourage low-rankness of the Hankel matrix.
result Hankel regularization enables optimal system recovery with fewer observations and better estimation rates.

Algorithm finds a simplified model for reinforcement learning under agent limitations.

problem Finding a simple model that approximates the true model for reinforcement learning.
method Uses rate-distortion theory to compute an approximately-value-equivalent, lossy compression of the environment.
result Proves an information-theoretic, Bayesian regret bound for the algorithm.

SAIL learns from sub-optimal demonstrations to improve sample efficiency in sparse reward tasks.

problem Reducing sample complexity in sparse-rewarded tasks.
method Self-Adaptive Imitation Learning (SAIL) that exploits sub-optimal demonstrations and efficient exploration.
result Significantly improved sample efficiency and better final performance across various tasks.

The paper sets fundamental limits for ERM in high dimensions.

problem Understanding statistical accuracy of ERM in high-dimensional settings.
method Sharp performance characterizations and tight lower bounds derived for generalized linear models.
result Optimal tuning of loss function and regularization parameter.

LinMED is a new linear bandit algorithm with near-optimal regret bound.

problem Optimizing decision-making in linear bandit problems with sub-Gaussian distributions.
method LinMED is a randomized linear bandit algorithm with closed-form arm sampling probabilities.
result LinMED achieves a near-optimal regret bound of dnd\sqrt{n} up to logarithmic factors.

Two efficient algorithms improve online item recommendation for large user-item matrices.

problem Low rank matrix completion in an online setting with noisy rewards.
method Phased algorithms extsc{PhasedClusterElim} and extsc{DeterminantElim} for item recommendation.
result Near-optimal per-user regret guarantees for item recommendation.

LEARN-SAM improves RL from sub-optimal demonstrations by localizing expert policies and selectively using demonstrations.

problem Improving RL from sub-optimal or sparse demonstrations.
method Local Ensemble and Reparameterization with Split and Merge of expert policies (LEARN-SAM).
result LEARN-SAM boosts learning speed and accuracy by selectively using demonstrations.

Paper establishes first instance-dependent lower bound for PAC reinforcement learning.

problem Identifying near-optimal policies in tabular MDPs with minimal samples.
method Proposes instance-dependent lower bound for sample complexity.
result Lower bound closely matches PEDEL algorithm's sample complexity.

The paper compares theoretical and empirical performance of imputation methods for missing data.

problem Missing data in real-world datasets.
method Contrast of theoretical and empirical imputation methods for prediction.
result Mean-imputation is asymptotically optimal for prediction, while mode-imputation is sub-optimal.

We address reinforcement learning problems with finite state and action spaces where the underlying MDP has some known structure that could be potentially exploited to minimize the exploration rates of suboptimal (state, action) pairs. For any arbitrary structure, we derive problem-specific regret lower bounds satisfie…

2018-06-03abs ↗pdf ↗

Study minimax off-policy evaluation in multi-armed bandits with known and unknown behavior policies.

problem Evaluate policies in multi-armed bandits with unknown behavior policies.
method Develop minimax rate-optimal procedures for known and unknown behavior policies, including the Switch estimator and Chebyshev polynomial-based estimator.
result Plug-in estimator achieves optimal competitive ratio up to a logarithmic factor when behavior policy is unknown.

Neural networks outperform NTK on compositional tasks, revealing a complexity gap.

problem Understanding the performance gap between neural networks and NTK on tasks with compositional structure.
method Characterized Fourier and architectural complexities, and analyzed the minimax rates of the architecture class.
result The NTK estimator is exponentially sub-optimal compared to the minimax floor when complexities decouple.

Paper improves risk bound for MTL with graph-dependent data.

problem Sub-optimal risk bound in multi-task learning with graph-dependent data.
method Proposes a new Bennett-type inequality and develops new Talagrand-type inequality and local fractional Rademacher complexity.
result Derives a sharper risk bound of O(lognn)O(\frac{\log n}{n}).