Develops new instance-optimality concepts in differential privacy.
problem Improving privacy guarantees in statistical estimation.
method Introduces local minimax risk and unbiased mechanisms, and develops inverse sensitivity mechanisms.
result Inverse sensitivity mechanisms are nearly instance optimal for a wide range of functions.
New algorithm achieves instance-optimality in decision making.
problem Develop adaptive algorithms for interactive decision making.
method Introduce Allocation-Estimation Coefficient (AEC) and develop A E 2 \mathsf{AE}^2 AE 2 algorithm. result First non-asymptotic instance-optimal performance guarantees.
Private density estimation in Wasserstein distance for geographic populations.
problem Private estimation of population density distributions.
method Differentially private algorithms for Wasserstein distance, instance-optimal.
result Uniformly achievable instance-optimal rates in both 1D and 2D.
Study binary hypothesis testing with privacy and communication constraints.
problem Binary hypothesis testing under local differential privacy and communication constraints.
method Qualifies results as minimax or instance optimal, develops instance-optimal algorithms.
result Achieves minimum possible sample complexity under both privacy and communication constraints.
Private KL distribution estimation improved with instance-optimality.
problem Minimizing KL divergence between true and estimated distributions.
method Construct minimax optimal private estimators, then focus on instance-optimality.
result Achieved instance-optimality up to constant factors for KL estimation.
We study the active learning problem of top- k k k ranking from multi-wise comparisons under the popular multinomial logit model. Our goal is to identify the top- k k k items with high probability by adaptively querying sets for comparisons and observing the noisy output of the most preferred item from each comparison. To ac…
New method improves learning from multiple correlated data trajectories.
problem Learning from multiple correlated data trajectories without mixing assumptions.
method Hellinger localization framework for maximum likelihood estimation.
result Instance-optimal bounds that scale with full data budget under broad conditions.
The research proposes a stopping rule for reinforcement learning algorithms based on instance-dependent confidence.
problem Dramatic variation in convergence rates of reinforcement learning algorithms due to problem structure.
method Develops instance-dependent confidence regions and a data-dependent stopping rule for MDP policy evaluation and optimal value estimation.
result Proposes a stopping rule that adapts to the instance-specific difficulty of the problem, allowing for early termination.
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.
New algorithm optimally evaluates policies with linear approximations.
problem Policy evaluation with linear function approximation.
method Accelerated, variance-reduced fast temporal difference algorithm (VRFTD).
result VRFTD matches both deterministic and stochastic lower bounds.
A new approach for instance-optimal learning that bypasses impossibility results.
problem Impossibility of achieving marginal-by-marginal guarantees for all marginals.
method Introduces relatively smart learning, which requires competition only with certifiable semi-supervised guarantees.
result One-Inclusion Graph learner is relatively smart up to squaring the sample complexity.
New algorithms for model selection in linear bandits adapt to instance complexity.
problem Adapting to the instance-dependent complexity of the true model in linear bandits.
method Design of algorithms in fixed confidence and fixed budget settings, leveraging experimental design and selection-validation procedures.
result Near instance optimal guarantees for model selection in linear bandits.
Optimal best-arm identification with known number of optimal arms.
problem Identifying the best arm in a multi-armed bandit with multiple optimal arms under fixed confidence.
method Deriving a new information-theoretic lower bound and proposing a modified stopping rule.
result Achieving asymptotic instance-optimality with a new lower bound and new stopping rule.
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.
Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.
problem Matrix Learning from Expert Advice problem.
method Developed a general potential-based framework for matrix LEA, using a new Jensen's trace inequality.
result Achieved instance-optimal regret bound of O ( T ⋅ S ( X ∣ ∣ d − 1 I d ) ) O(\sqrt{T\cdot S(X||d^{-1}I_d)}) O ( T ⋅ S ( X ∣∣ d − 1 I d ) ) . New method estimates optimal Q-values with better accuracy for specific problems.
problem Estimating optimal Q-values in reinforcement learning is difficult and varies by problem instance.
method Local minimax framework and variance-reduced Q-learning.
result Sharp lower bounds on estimation accuracy for Q-learning.
Simple method for estimating missing panel data entries with confidence intervals.
problem Estimating missing values in panel data with staggered adoption.
method Simple matrix algebra and singular value decomposition for estimation, with data-driven confidence intervals.
result Confidence intervals match non-asymptotic lower bounds, proving instance optimality.
This paper improves signal reconstruction using determinantal sampling from random nodes.
problem Approximating square-integrable functions from random node evaluations.
method Combines determinantal point processes and mixtures thereof for RKHS-adapted approximations.
result Proves mean-square guarantees in L 2 L^2 L 2 norm and shows faster convergence rates. Characterizes statistical complexity of realizable regression in PAC and online learning.
problem Understanding the statistical complexity of realizable regression in both PAC and online learning settings.
method Introduces minimax instance optimal learners, novel and combinatorial dimensions to characterize learnability.
result Characterizes which classes of real-valued predictors are learnable and provides necessary conditions for learnability.
Improved stochastic optimization outperforms standard methods.
problem Optimizing smooth, strongly convex functions with noisy data.
method Variance reduction strategy called VISOR.
result VISOR achieves optimal sample complexity and oracle complexity.
Study optimizes estimating linear functionals from observational data without strict overlap.
problem Estimating linear functionals from observational data with strict overlap assumption violated.
method Kernel-based approach for non-asymptotic local minimax bounds.
result Achieves optimal risk for estimating linear functionals in observational data.
New methods reduce private federated learning communication automatically.
problem Reducing communication in private federated learning.
method Automatic compression rate adjustment based on training error, using secure aggregation and differential privacy.
result Provable instance-optimal for mean estimation, achieving favorable compression rates.
We investigate the optimality of perturbation based algorithms in the stochastic and adversarial multi-armed bandit problems. For the stochastic case, we provide a unified regret analysis for both sub-Weibull and bounded perturbations when rewards are sub-Gaussian. Our bounds are instance optimal for sub-Weibull pertur…
Optimizes budgeted evaluations of LLMs by allocating queries to judges efficiently.
problem Evaluating LLMs with heterogeneous judges and varying costs and reliability.
method Formalizes and analyzes budgeted heteroskedastic multi-judge estimation, proposing EST-IVWE for practical implementation.
result EST-IVWE matches the oracle IVWE rate up to lower-order terms in the budget and is instance-optimal.
Study bounds noise level in linear regression with dependent data.
problem Analyzing noise level in linear regression with dependent data.
method Derive upper bounds for random design linear regression with β β β -mixing data, without realizability assumptions. result Correctly recovers the noise level of the problem, exhibiting graceful degradation with misspecification.
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.
New algorithm identifies best arm in semiparametric bandits with near optimal efficiency.
problem Fixed-confidence Best Arm Identification in semiparametric bandits with unknown baseline shift.
method Phase-elimination algorithm based on orthogonalized regression design.
result Nearly optimal high-probability sample-complexity upper bound established.
In the Best- k k k -Arm problem, we are given n n n stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the k k k arms with the largest means by taking as few samples as possible. In this paper, we make progress towards a complete characterization of the instance-wise sample…
New algorithm reduces ERM problem size while maintaining accuracy.
problem Empirical risk minimization problem size reduction.
method Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm.
result Uniform ( 1 ± ε ) (1\pm\varepsilon) ( 1 ± ε ) relative-error approximation for ERM objective. 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.
Adaptive online learning algorithm improves history forgetting in nonstationary environments.
problem Adversarial nonstationary environments where future data can be very different from past data.
method Discounted regret in online convex optimization, FTRL-based algorithm, adaptive learning rate.
result Improves classical gradient descent with constant learning rate in online convex optimization.
VRCQ algorithm reduces variance in Q-learning for MDPs, achieving optimal sample complexity.
problem Estimating the optimal Q-function in MDPs with synchronous sampling.
method VRCQ combines direct variance reduction and Cascade Q-learning.
result VRCQ is minimax optimal and instance optimal for single-action problems.
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 best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly "amplify" the effective amount of data available. For a large variety of distri…
New algorithm IAC recovers hidden communities in labeled SBM with optimal performance.
problem Recovering hidden communities in Labeled Stochastic Block Model with varying cluster sizes.
method IAC (Instance-Adaptive Clustering) algorithm, consisting of spectral clustering and iterative likelihood-based improvements.
result IAC achieves optimal performance matching instance-specific lower bounds in expectation and with high probability.
HyperLISTA simplifies LISTA training with adaptive hyperparameters.
problem Sparse recovery with LISTA networks.
method Adaptive hyperparameter tuning based on previous layers.
result HyperLISTA achieves similar performance on seen data and better on unseen data.
LinFACT identifies all ε-best arms in linear bandits with near-optimal efficiency.
problem Efficiently identifying multiple optimal candidates in high trial-and-error cost tasks.
method LinFACT algorithm designed for linear bandits, with information-theoretic lower bound and upper bound derivation integration.
result LinFACT achieves instance optimality, matching lower bound up to a logarithmic factor.
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive (or random) linear…
New algorithm improves online learning with reduced discretization.
problem Improving adaptive online learning with refined discretization.
method Continuous time approach to online learning, followed by a new discretization argument.
result Optimal regret bound with O ( V T ) O(\sqrt{V_T}) O ( V T ) dependence on gradient variance. Study optimal and instance-dependent guarantees for solving linear equations with Markovian data.
problem Approximately solving linear fixed point equations with Markovian data.
method Non-asymptotic bounds and instance-dependent characterizations for stochastic approximation.
result Instance-optimality of the averaged SA estimator and matching upper and lower bounds.
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.
Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.
problem Optimizing risk-averse bandit problems with sub-Gaussian rewards.
method Anchor-free nonparametric Thompson Sampling algorithm ρ e x t − N P T S S G ρ ext{-}NPTS_{\mathrm{SG}} ρ e x t − N P T S SG . result Achieves regret matching the instance-dependent lower bound to leading order in log n \log n log n . Study task-guided exploration in linear dynamical systems, improving sample complexity.
problem Efficiently learning about an environment to complete a specific task.
method Proposed a computationally efficient experiment-design based exploration algorithm.
result Optimally explores the environment, collecting precise information needed to complete the task.
New framework improves differential privacy for asymmetric datasets.
problem Improving differential privacy for asymmetric datasets.
method Adapts inverse sensitivity mechanism with sparse vector technique.
result Efficiently estimates general functions with improved privacy.
We learn sparse precision matrices from compressed data sketches.
problem Learning a graph from high-dimensional data with limited storage.
method Estimate a sparse precision matrix from a sketch of the data using non-linear random features.
result It is possible to estimate a sparse precision matrix from a sketch of size $m=Ω\left((d+2k)\log(d)
ight)$ .
We consider PAC-learning a good item from k k 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…
Study robust estimation of principal components under adversarial perturbations.
problem Estimating principal components in high-dimensional data under adversarial perturbations.
method Design of a computationally efficient algorithm for recovering the top-r principal subspace.
result The algorithm recovers an estimate of the top-r principal subspace with error depending on the robustness parameter κ.
A learning algorithm optimizes SOR solver parameters for a sequence of linear systems efficiently.
problem Optimizing solver parameters for a sequence of related linear systems without extra computations.
method Bandit and contextual bandit algorithms for online learning of optimal parameters.
result The overall cost approaches the best fixed parameter as the sequence length increases.