New algorithm reduces contextual bandit identification to argmax calls.
problem Best-arm identification in stochastic contextual bandits.
method Instance-optimal PAC algorithm using argmax oracle calls.
result First instance-dependent PAC sample complexity for contextual bandits.
New method for identifying best designs in vector optimization with uncertain feedback.
problem Optimizing vector-valued outcomes with uncertain preferences.
method Stochastic bandit feedback, polyhedral ordering cone, (ε,δ)-PAC Pareto set identification. result Sample complexity characterized and matched by the naïve elimination algorithm.
Efficiently identifies best policies in tabular MDPs with reduced computational cost.
problem Identifying the best policy in tabular MDPs with high computational cost.
method Combines posterior sampling with online learning to achieve asymptotic optimality.
result Achieves optimal sample complexity and posterior contraction rate with O(S2AH) per episode. Algorithm identifies Pareto set in bandits with contaminated feedback.
problem Identifying Pareto set in multi-objective bandits with adversarial contamination.
method Sample median-based multi-objective adaptive elimination algorithm.
result Sample complexity bound that depends on contamination probability.
Paper derives PAC-Bayesian bounds for LTI systems learning from empirical data.
problem Characterizing predictive power of LTI systems learned from data.
method PAC-Bayesian bounds for LTI stochastic dynamical systems with inputs.
result Finite-sample error bounds for learning algorithms of LTI systems.
PAC best arm identification with a deadline, improving efficiency over sequential methods.
problem Identifying an optimal arm under a fixed time constraint.
method Elastic Batch Racing (EBR) algorithm for (ε,δ)-PAC best arm identification under a deadline. result EBR is optimal with respect to two hardness results and outperforms sequential methods.
Improves model accuracy for neural nets in stochastic dynamics with partial prior knowledge.
problem Stability and accuracy in neural nets modeling stochastic dynamics with many parameters.
method Three steps: probabilistic weights, partial knowledge incorporation, and PAC-Bayesian training.
result Improved model fit with partial and noisy prior knowledge.
PROBE optimizes best-arm identification with cheap proxies, improving sample complexity.
problem Fixed-confidence best-arm identification with costly rewards and correlated cheap proxies.
method PROBE uses control-variate adjustment and phase elimination to learn residual variance online.
result PROBE achieves oracle sample complexity up to a constant factor and additive calibration cost.
New algorithm for efficiently identifying the best arm in stochastic bandits.
problem Best arm identification in stochastic multi-armed bandits with fixed confidence.
method Sequential probability ratio tests for arm selection.
result Asymptotically optimal sample complexity and guaranteed δ−PAC performance. 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.
Paper establishes new lower bounds for MDPs with changing transition kernels.
problem Minimizing sample complexity and regret in non-stationary MDPs.
method Developed novel lower bounds and constructed hard MDPs.
result Proved Ω((H3SA/ε2)log(1/δ)) sample complexity lower bound. The study analyzes group testing algorithms for identifying defective items with high confidence.
problem Identifying defective items from a population using group testing with high confidence.
method Formulated as a function learning problem using the PAC framework, analyzed three algorithms: column matching, combinatorial basis pursuit, and definite defectives.
result Derived bounds on the number of tests needed for approximate set identification, comparing with existing bounds and simulating performance.
State of the art online learning procedures focus either on selecting the best alternative ("best arm identification") or on minimizing the cost (the "regret"). We merge these two objectives by providing the theoretical analysis of cost minimizing algorithms that are also delta-PAC (with a proven guaranteed bound on th…
PAC-MCTS addresses biased search in LLM-guided planning by dynamically pruning.
problem Systematic biases in LLMs lead to inefficient and unsafe search in deep planning tasks.
method Formulates node expansion as BAI under bounded bias, derives sample complexity bounds, and proposes PAC-MCTS for dynamic confidence bounds.
result PAC-MCTS improves robustness and efficiency by up to 78% fewer API evaluations and 3x higher sample efficiency.
New algorithm reduces sample complexity for multi-task bandits.
problem Optimizing representation and predictor pairs for multi-task bandits.
method OSRL-SC algorithm with sample complexity H(Glog(1/δG)+Xlog(1/δH)). result OSRL-SC algorithm approaches sample complexity lower bounds.
Formalizes identifying information to answer key questions about machine learning from uncertain and novel observations.
problem Understanding and quantifying information from uncertain and novel observations in machine learning.
method Formalizes identifying information, defines hypothesis identification and sample complexity, and proves sample complexity properties for various data-generating processes.
result Proves the information theoretic characteristics of hypothesis identification and sample complexity, and shows how to compute identifying information and novel information.
New reinforcement learning algorithm achieves instance-optimal sample complexity.
problem Achieving low regret and identifying optimal policies in reinforcement learning.
method A novel planning-based algorithm that explicitly accounts for state visitation distributions.
result The proposed algorithm attains nearly minimax optimal sample complexity, improving over worst-case bounds.
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.
We consider PAC-learning a good item from k-subsetwise feedback information sampled from a Plackett-Luce probability model, with instance-dependent sample complexity performance. In the setting where subsets of a fixed size can be tested and top-ranked feedback is made available to the learner, we give an algorithm w…
We consider the problem of near-optimal arm identification in the fixed confidence setting of the infinitely armed bandit problem when nothing is known about the arm reservoir distribution. We (1) introduce a PAC-like framework within which to derive and cast results; (2) derive a sample complexity lower bound for near…
New complexity measure helps in agnostic reinforcement learning with or without access to MDP dynamics.
problem Understanding the number of rounds needed to learn an ε-suboptimal policy in unknown MDPs.
method Introducing spanning capacity as a new complexity measure and developing POPLER algorithm.
result There is a separation between generative and online access models for agnostic learnability.
We consider the problem of identifying any k out of the best m arms in an n-armed stochastic multi-armed bandit. Framed in the PAC setting, this particular problem generalises both the problem of `best subset selection' and that of selecting `one out of the best m' arms [arcsk 2017]. In applications such as crowd…
Adaptive exploration scheme for evaluating multiple policies with different rewards.
problem Online multi-reward multi-policy evaluation.
method Adapted (ε,δ)-PAC perspective and MR-NaS exploration scheme to minimize sample complexity. result Demonstrated effectiveness of adaptive exploration in tabular domains.
The OLS estimator optimally identifies stable linear systems with a finite number of samples.
problem Identifying stable linear systems with a finite number of samples.
method Finite-time analysis of the Ordinary Least Squares (OLS) estimator for stable linear systems.
result The OLS estimator achieves optimal sample complexity for stable systems, matching existing lower bounds up to universal factors.
PAC-Bayesian bounds for MLPs with cross entropy loss validated.
problem Generalization bounds for MLPs with cross entropy loss.
method Introduced probabilistic explanations and proved PAC-Bayesian bounds using ELBO.
result MLPs with cross entropy loss inherently guarantee PAC-Bayesian generalization bounds.
Unified derivation of PAC-Bayes and MI bounds for general VC classes with fast rates.
problem Generalization bounds for machine learning models with VC classes.
method Unified derivation of conditional PAC-Bayesian and mutual information bounds, including MAC-Bayesian bounds.
result Nontrivial bounds for general VC classes and faster rates for specific conditions.
The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by viewing Gibbs classifiers as linear operators. The goal of this paper is to extend thi…
PAC-Wrap provides provable guarantees for semi-supervised anomaly detection.
problem Ensuring reliable anomaly detection in safety-critical applications.
method PAC-Wrap wraps around existing anomaly detection methods to provide PAC guarantees.
result PAC-Wrap effectively provides rigorous guarantees for various anomaly detectors.
Survey and compare PAC-Bayes bounds for bandit problems.
problem Designing and evaluating bandit algorithms with strong performance guarantees.
method PAC-Bayes bounds applied to bandit problems.
result PAC-Bayes bounds useful for offline bandit algorithms, but loose for online algorithms.
Statistical performance bounds for reinforcement learning (RL) algorithms can be critical for high-stakes applications like healthcare. This paper introduces a new framework for theoretically measuring the performance of such algorithms called Uniform-PAC, which is a strengthening of the classical Probably Approximatel…
Efficient PAC learning for contrastive linear representations is achieved.
problem Efficient PAC learning for contrastive linear representations.
method Relaxing the problem to a semi-definite program and using Rademacher complexity.
result First efficient PAC learning algorithm for contrastive learning.
This research improves PAC-Bayesian bounds for classification tasks using convexified loss.
problem Deriving generalization bounds for classification tasks with non-convex loss functions.
method Shift focus to misclassification excess risk bounds for PAC-Bayesian classification using convex surrogate loss and leveraging PAC-Bayesian relative bounds in expectation.
result Improved PAC-Bayesian bounds for classification tasks with convex surrogate loss.
Meta-learning bounds derived using PAC-Bayes theory for improved generalization.
problem Uncertainty in generalization performance for meta-learning with new tasks.
method PAC-Bayes relative entropy bounds and empirical risk minimization (ERM) method.
result Competitive generalization performance and rapid convergence with data-dependent prior.
PAC-Bayes framework fails on simple 1D linear classification task.
problem Proving the learnability of simple 1D linear classification tasks using PAC-Bayes bounds.
method Demonstrated a specific 1D linear classification task that PAC-Bayes cannot analyze.
result PAC-Bayes framework cannot prove learnability of simple 1D linear classification tasks.
New algorithm optimizes PAC-Bayes bound without surrogate loss.
problem Mismatch between optimisation objective and generalisation bound in stochastic neural networks.
method Proposes a novel training algorithm that optimizes the PAC-Bayesian bound directly.
result Empirical results show improved performance over existing PAC-Bayesian training methods.
Introduces PAC-Bayes bounds for understanding learning procedures.
problem Understanding the generalization ability of learning procedures.
method PAC-Bayesian bounds and their applications to neural networks.
result Simplified version of localization technique described.
PAC-Bayes bound requires prior to place mass on high-performing predictors.
problem Explaining generalization in machine learning.
method Analyzing necessary conditions for PAC-Bayes bounds to provide meaningful generalization guarantees.
result Achieving a target generalisation level requires the prior to place sufficient mass on high-performing predictors.
New PAC-Bayesian bounds for online learning with data streams.
problem Challenges of traditional PAC-Bayesian bounds in dynamic data collection.
method Developed new PAC-Bayesian bounds in online learning framework, using updated regret definition and batch-to-online conversion.
result PAC-Bayesian bounds hold for online learning with dependent data and non-convex losses.
New method reduces computational cost for estimating PAC-Bayes bounds.
problem High computational cost in estimating PAC-Bayes bounds.
method General alternative method that makes computational savings.
result Reduces computational cost on the order of the dataset size.
New algorithms reduce communication costs in collaborative learning.
problem Reducing communication costs in collaborative learning.
method Distributed boosting and adaptation to classification noise.
result Communication-efficient algorithms for collaborative PAC learning robust to noise.
Paper develops PAC verification for hypothesis classes and statistical algorithms.
problem Verifying machine learning models interactively.
method Develops interactive proof for PAC verification, proves lower bounds, and introduces a generalization.
result Improved protocol for verifying unions of intervals and statistical query algorithms.
Algorithm identifies the best arm in linear bandits with high probability.
problem Best arm identification in linear multi-armed bandits with noisy measurements.
method Phased Elimination Linear Exploration Game (PELEG) using no-regret learners.
result PELEG achieves sample complexity matching lower bounds.
This paper improves meta-learning by developing new PAC-Bayes bounds.
problem Meta-learning generalization gap across multiple tasks.
method Upper bounding convex functions linking environment and task-level losses.
result New PAC-Bayes bounds for meta-learning with improved algorithms.
New PAC-Bayes training method improves model generalization for unbounded loss.
problem Improving generalization of complex models under unbounded loss.
method Established new PAC-Bayes bound for unbounded loss, jointly training prior and posterior.
result Outperforms existing PAC-Bayes training algorithms and matches ERM accuracy.
New PAC-Bayes bounds use Wasserstein distances to improve generalization.
problem Lack of geometric properties in existing PAC-Bayes bounds.
method Developed new PAC-Bayes bounds with Wasserstein distances.
result Optimization guarantees translate to good generalization abilities.
PAC-Bayesian framework for fairness in stochastic and deterministic classifiers.
problem Theoretical guarantees on fairness for balancing predictive risk and fairness constraints.
method PAC-Bayesian framework for both stochastic and deterministic classifiers, covering a broad class of fairness measures.
result Derives generalization bounds for fairness, demonstrating tightness with empirical evaluation.
Researchers estimate optimal PAC-Bayes bounds using Hamiltonian Monte Carlo.
problem Estimating tight PAC-Bayes bounds with restricted posterior families.
method Sampling from optimal Gibbs posterior using Hamiltonian Monte Carlo, estimating KL divergence, and proposing high-probability bounds.
result Significant tightness gaps in PAC-Bayes bounds, up to 5-6% in some cases.
New empirical PAC-Bayes bound for Markov chains with finite state space.
problem Lack of empirical bounds for Markov chains with temporal dependence.
method Proved a new PAC-Bayes bound for Markov chains, providing an empirical pseudo-spectral gap.
result First fully empirical PAC-Bayes bound for Markov chains with finite state space.