Efficient streaming algorithms for robust statistics with near-optimal memory.
problem High-dimensional robust statistics tasks in streaming model.
method First efficient streaming algorithms with near-optimal memory requirements.
result Near-optimal error guarantees and space complexity nearly-linear in the dimension for robust mean estimation.
AE-LSVI identifies near-optimal policies in complex systems with minimal data.
problem Identifying near-optimal policies in complex, costly data acquisition systems.
method Combines optimism and pessimism for active exploration in a generative model setting.
result Proves near-optimal policy identification over entire state spaces with polynomial sample complexity.
Algorithm extsc{Pedel} learns near-optimal policies efficiently on specific problems.
problem Learning near-optimal policies in linear MDPs with minimal samples.
method Online experiment design to focus exploration on relevant directions.
result Achieves instance-dependent complexity, outperforming minimax-optimal algorithms.
New algorithm detects changes quickly without knowing parameters, near optimally.
problem Quickest change detection with unknown parameters.
method Leverages theoretical asymptotic properties to derive a scalable approximate algorithm with near optimal performance.
result Detects changes in constant complexity with near optimal performance.
New algorithm learns halfspaces with membership queries, achieving near optimal label complexity.
problem Learning halfspaces with membership queries.
method Proposed a new algorithm for learning halfspaces with membership queries, proving near optimal label complexity.
result Achieves near optimal label complexity for learning halfspaces.
Study on learning sparse fixed-structure Gaussian Bayesian networks with near-optimal sample complexity.
problem Learning a fixed-structure Gaussian Bayesian network up to a bounded error in total variation distance.
method Analysis of node-wise least squares regression and introduction of BatchAvgLeastSquares and CauchyEst algorithms.
result BatchAvgLeastSquares and CauchyEstTree have near-optimal sample complexity.
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, …
New bounds for private learning of high-dimensional Gaussian distributions.
problem Learning high-dimensional Gaussian distributions under differential privacy constraints.
method Analytic tools for constructing global covers from local covers, modified hypothesis selection techniques.
result Near-optimal sample complexity bounds for general Gaussians, conjectured to be near-optimal in the general case.
A method for robust reinforcement learning in large state spaces.
problem Challenges in RL with large state spaces, costly data, and real-world dynamics deviation.
method Distributionally robust Markov decision processes with Gaussian Processes and maximum variance reduction.
result Efficient learning of multi-output nominal transition dynamics with statistical sample complexity bounds.
Paper studies S-rectangular DR-RL models for robust reinforcement learning with near-optimal sample complexity.
problem Addressing distributional discrepancies in reinforcement learning environments.
method Empirical value iteration algorithm for divergence-based S-rectangular DR-RL models.
result Near-optimal sample complexity bound of O ( ∣ S ∣ ∣ A ∣ ( 1 − γ ) − 4 ε − 2 ) O(|\mathcal{S}||\mathcal{A}|(1-γ)^{-4}\varepsilon^{-2}) O ( ∣ S ∣∣ A ∣ ( 1 − γ ) − 4 ε − 2 ) . Near-optimal rates for multi-task learning with shared representations.
problem Approximation and statistical complexity of learning multiple operators.
method Multiple Neural Operators (MNO) architecture and comparison with DeepONet.
result Near-optimal upper and lower bounds for approximation and generalization.
ODCGM solves non-convex optimization on manifolds with simpler projections.
problem Minimizing non-convex functions over smooth manifolds.
method Orthogonal Directions Constrained Gradient Method (ODCGM) that projects onto a vector space.
result ODCGM converges to the manifold with near-optimal oracle complexities.
New algorithms ensure reproducibility and optimal convergence in convex optimization.
problem Trade-off between reproducibility and convergence rate in convex optimization.
method Regularization-based algorithms for smooth convex minimization and minimax optimization.
result Achieves optimal reproducibility and near-optimal gradient complexity for various oracle settings.
Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.
problem Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
method Near-optimal algorithms with optimal error guarantees, achieving sample complexity n = i l d e O ( d / ε 2 ) n = ilde{O}(d/ε^2) n = i l d e O ( d / ε 2 ) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an accuracy-dependent stepsize that slows down the convergence in practice, and cannot handle objec…
New algorithm achieves near optimal sample complexity for 1-identification problem.
problem Determining if an arm's mean reward is at least a known threshold with high probability.
method Design of Sequential-Exploration-Exploitation (SEE) algorithm with non-asymptotic analysis.
result Achieves near optimality in sample complexity, matching upper and lower bounds up to a polynomial logarithmic factor.
New RL method reduces sample complexity for large policy spaces.
problem Large-scale RL with unknown optimal policies and state/action spaces.
method Introduces eluder dimension for policy space, proving near-optimal sample complexity.
result Near-optimal sample complexity upper bound that depends linearly on eluder dimension.
Near-optimal algorithms for predicting across multiple loss functions efficiently.
problem Predicting optimally across various loss functions simultaneously.
method Developed near-optimal online and offline learning algorithms for omniprediction.
result Achieved near-optimal complexity for both online and offline settings.
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and time-efficient estimators for all sufficiently smooth, symmetric and non-symmetric, …
This paper optimizes model-based RL for two-player zero-sum games with near-optimal sample complexity.
problem Optimizing model-based reinforcement learning for two-player zero-sum games with minimal samples.
method Model-based reinforcement learning approach for two-player discounted zero-sum Markov games with a generative model.
result Achieves a sample complexity of i l d e O ( ∣ S ∣ ∣ A ∣ ∣ B ∣ ( 1 − γ ) − 3 ε − 2 ) ilde O(|S||A||B|(1-γ)^{-3}ε^{-2}) i l d e O ( ∣ S ∣∣ A ∣∣ B ∣ ( 1 − γ ) − 3 ε − 2 ) for finding the Nash equilibrium and ε-NE policies. This paper optimizes sampling for least-squares approximation.
problem Optimizing sampling for least-squares approximation in arbitrary linear spaces.
method Introducing the Christoffel function to construct near-optimal random sampling strategies.
result The number of samples scales log-linearly in the dimension of the approximation space.
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor γ ∈ ( 0 , 1 ) γ\in(0,1) γ ∈ ( 0 , 1 ) we provide an algorithm that computes an ε ε ε -optimal strategy with high-probability given $\tilde{O}((1 - γ)^{-3}…
Improved sample complexity for learning halfspaces with malicious noise.
problem Efficiently learning halfspaces in the presence of malicious noise.
method New analysis of Awasthi et al. algorithm with matrix Chernoff inequality and localization schemes.
result Achieved near-optimal sample complexity of i l d e O ( d ) ilde{O}(d) i l d e O ( d ) for isotropic log-concave distributions. Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution.
problem Characterizing measurement complexity for signals from any prior distribution, including the entire space.
method Characterization of measurement complexity using posterior sampling estimator for Gaussian measurements and any prior distribution.
result Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution, robust to model mismatch.
It has been a long-standing problem to efficiently learn a halfspace using as few labels as possible in the presence of noise. In this work, we propose an efficient Perceptron-based algorithm for actively learning homogeneous halfspaces under the uniform distribution over the unit sphere. Under the bounded noise condit…
Efficiently find near-optimal medical treatments with less trial and error.
problem Finding effective medical treatments through trial and error.
method Formalizes the problem, uses a causal inference framework, and proposes model-based dynamic programming and greedy algorithms.
result Our methods compare favorably to model-free reinforcement learning, offering a more transparent trade-off between search time and treatment efficacy.
Paper introduces DP TDA for near-optimal private persistence diagrams.
problem Challenges in privatizing topological data analysis.
method Sensitivity analysis of persistence diagrams, use of exponential mechanism.
result Proposes near-optimal privacy mechanism for TDA.
Improved algorithm for adaptive dueling bandits with near-optimal regret bound.
problem Non-stationary dueling bandits with unknown number of preference changes.
method Elimination-based rescheduling algorithm for adaptive dynamic regret.
result Near-optimal i l d e O ( S e x t t t C W T ) ilde{O}(\sqrt{S^{ exttt{CW}} T}) i l d e O ( S e x ttt C W T ) dynamic regret bound. Paper tackles offline CMDP problems with near-optimal algorithm and sample complexity bound.
problem Offline CMDP problems with only offline data available.
method DPDL algorithm using single-policy concentrability coefficient C ∗ C^* C ∗ and deviation control mechanism. result DPDL algorithm matches sample complexity lower bound with i l d e O ( ( 1 − γ ) − 1 ) ilde{\mathcal{O}}((1-γ)^{-1}) i l d e O (( 1 − γ ) − 1 ) factor. We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others. Our approach is to directly estimate the low-rank factor …
Pessimistic Q-learning improves sample efficiency in offline reinforcement learning.
problem Insufficient coverage and sample scarcity in offline reinforcement learning datasets.
method Pessimistic Q-learning algorithm for offline reinforcement learning, focusing on variance reduction.
result Near-optimal sample complexity achieved with the proposed algorithm.
We decode latent states in Block MDPs and learn near-optimal policies.
problem Model estimation and reward-free learning in Block MDPs.
method Information-theoretical lower bound and efficient model estimation algorithm.
result Our algorithm approaches the information-theoretical limit for latent state decoding and converges to optimal policies.
Gaussian processes (GP) are a well studied Bayesian approach for the optimization of black-box functions. Despite their effectiveness in simple problems, GP-based algorithms hardly scale to high-dimensional functions, as their per-iteration time and space cost is at least quadratic in the number of dimensions d d d and i…
Improved private agnostic learning with near-optimal sample complexity.
problem Private agnostic learning with arbitrary privacy parameters.
method Near-optimal sample complexity construction.
result Near-optimal extra sample complexity of \(\widetilde{O}(\mathrm{VC}(\mathcal{C})/α^2)\) for any \(\varepsilon \leq 1\).
New bounds for learning near-optimal policies in CMDPs with constraints.
problem Optimizing policies in CMDPs with constraints.
method Model-based algorithm addressing relaxed and strict feasibility.
result Near-optimal sample complexity bounds for CMDPs.
New algorithm solves complex optimization problems efficiently.
problem Minimizing convex upper-level functions over optimal lower-level solutions.
method Reformulates bilevel problems into functionally constrained problems, achieving near-optimal rates.
result Achieves near-optimal rates for both smooth and nonsmooth problems.
Efficiently learns halfspaces with malicious noise, near-optimal label complexity.
problem Learning s s s -sparse halfspaces under malicious label noise. method Active learning algorithm with instance reweighting and empirical risk minimization.
result Near-optimal label complexity of O ( s log 4 d / ε ) O(s \log^4 d / ε) O ( s log 4 d / ε ) and noise tolerance Ω ( ε ) Ω(ε) Ω ( ε ) . New method finds near-optimal solutions for non-convex optimization problems.
problem Finding near-optimal solutions for non-convex optimization problems.
method Riemannian stochastic recursive momentum method
result Achieves a near-optimal complexity of i l d e O ( ε − 3 ) ilde{\mathcal{O}}(ε^{-3}) i l d e O ( ε − 3 ) . Framework reduces contextual bandit learning to offline regression with near-optimal regret.
problem Efficient learning with large action spaces and complex reward functions.
method Offline Estimation to Decisions (OE2D) algorithm that minimizes regret with near-optimal oracle calls.
result Near-optimal regret for contextual bandits with large action spaces and O ( l o g ( T ) ) O(log(T)) O ( l o g ( T )) offline oracle calls. New framework for DP-SMO with near-optimal privacy-loss trade-off.
problem Optimal trade-off between privacy and population loss in DP-SMO.
method General framework using Phased-ERM method and black-box optimization.
result Near-linear time algorithms with near-optimal guarantees.
In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed con…
New algorithm learns halfspaces with near-optimal sample complexity in noisy conditions.
problem Learning margin halfspaces with Massart noise.
method Computational efficient algorithm using online SGD on carefully selected convex losses.
result Sample complexity of Θ ~ ( 1 / ( γ 2 ε 2 ) ) \widetilde{\Theta}(1/(γ^2 ε^2)) Θ ( 1/ ( γ 2 ε 2 )) , nearly matching lower bound. Improved linear regression with privacy and robustness guarantees.
problem Private and robust linear regression with adversarial corruption.
method Differentially private stochastic gradient descent with full-batch gradient descent and adaptive clipping.
result Near optimal sample complexity for both private and robust linear regression.
OE2D framework reduces contextual bandits to offline regression for near-optimal regret.
problem Efficiently learning contextual bandits with large action spaces and complex reward functions.
method Offline Estimation to Decisions (OE2D) algorithm that reduces contextual bandits to offline regression.
result Near-optimal regret for contextual bandits with large action spaces and O ( log T ) O(\log T) O ( log T ) calls to an offline regression oracle. 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…
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.
Study near-optimal bounds for learning Gaussian halfspaces with random noise.
problem Learning general halfspaces with Gaussian distribution and random classification noise.
method Established nearly-matching algorithmic and SQ lower bounds, developed a computationally efficient learning algorithm.
result Sample complexity of learning algorithm is O ( d / ε + d / ( max { p , ε } ) 2 ) O(d/ε + d/(\max\{p, ε\})^2) O ( d / ε + d / ( max { p , ε } ) 2 ) , SQ lower bound is Ω ( d 1 / 2 / ( max { p , ε } ) 2 ) Ω(d^{1/2}/(\max\{p, ε\})^2) Ω ( d 1/2 / ( max { p , ε } ) 2 ) . Model-based Bayesian Reinforcement Learning (BRL) allows a found formalization of the problem of acting optimally while facing an unknown environment, i.e., avoiding the exploration-exploitation dilemma. However, algorithms explicitly addressing BRL suffer from such a combinatorial explosion that a large body of work r…