New method gives high confidence bounds for stochastic convex optimization with minimal overhead.
problem Rare high probability guarantees in stochastic convex optimization.
method ProxBoost algorithm combining robust distance estimation and proximal point method.
result Wide class of stochastic optimization algorithms can achieve high confidence bounds with logarithmic and polylogarithmic overhead.
In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance bounds in the inverse reinforcement learning setting---where the true reward fun…
Paper defines and solves a problem in representation learning to ensure fairness with high confidence.
problem Learning fair representations with high confidence guarantees for all downstream tasks.
method Formally defines the problem, introduces FRG framework, proves high probability fairness, and demonstrates effectiveness empirically.
result FRG framework provides high-confidence guarantees for limiting unfairness across all downstream models and tasks.
For an autonomous agent, executing a poor policy may be costly or even dangerous. For such agents, it is desirable to determine confidence interval lower bounds on the performance of any given policy without executing said policy. Current methods for exact high confidence off-policy evaluation that use importance sampl…
Paper proposes efficient data-driven confidence bands for distributed nonparametric regression.
problem High computational complexity in nonparametric regression for large datasets.
method Divide and conquer approach, averaging local estimates, with data-driven uncertainty quantification.
result Frequentist L 2 L_2 L 2 -confidence bands and minimax-optimal high-probability bounds for averaged estimator. Classifiers used in the wild, in particular for safety-critical systems, should not only have good generalization properties but also should know when they don't know, in particular make low confidence predictions far away from the training data. We show that ReLU type neural networks which yield a piecewise linear cla…
Algorithm constructs confidence sets for deep neural networks with PAC guarantees.
problem Ensuring reliable predictions for deep neural networks with high confidence.
method Combines calibrated prediction and learning theory bounds.
result Constructs PAC confidence sets for various deep models.
Estimating the value function for a fixed policy is a fundamental problem in reinforcement learning. Policy evaluation algorithms---to estimate value functions---continue to be developed, to improve convergence rates, improve stability and handle variability, particularly for off-policy learning. To understand the prop…
Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.
problem Minimizing regret in Gaussian process bandit optimization.
method Gaussian process upper confidence bound (GP-UCB) algorithm with refined analysis.
result Achieves O ( T ln 2 T ) O(\sqrt{T \ln^2 T}) O ( T ln 2 T ) cumulative regret under squared exponential kernel. Bayesian methods improve drug discovery experiment design.
problem Optimizing drug screening experiments in high-dimensional data.
method Bayesian inference and optimisation with upper confidence bound algorithms, Thompson sampling, and sparse tree search.
result Sparse tree search techniques outperform other methods in drug toxicity screening.
We provide a pointwise confidence bound for non-linear least-squares with fixed design.
problem Confidence estimation in non-linear ℓ 2 \ell^2 ℓ 2 -regularized least squares. method Pointwise confidence bound for local minimizers, using weighted norm involving inverse-Hessian.
result The proposed confidence bound scales with the test input's similarity to the training data.
B-REX efficiently learns Atari game policies from pixel inputs using Bayesian methods.
problem Learning reward functions from visual inputs with uncertainty and safety considerations.
method Bayesian Reward Extrapolation (B-REX) using successor features and preferences.
result B-REX generates posterior samples efficiently, enabling high-confidence performance bounds.
New method for rigorous confidence intervals in off-policy evaluation.
problem Evaluate new policies from off-policy data without executing them.
method Variational framework using kernel Bellman loss.
result Efficient method for tight confidence intervals in various settings.
Paper proposes sparse classification method for high-dimensional data.
problem Sparse classification in high-dimensional data with positive-confidence samples.
method Developed a novel sparse-penalization framework using L1, SCAD, and MCP penalties for convex and non-convex shrinkage.
result Proved near minimax-optimal sparse recovery rates under Restricted Strong Convexity condition.
We shrink confidence sets for equivalent discrete distributions using permutation equivalence.
problem Building high-probability confidence sets for equivalent discrete distributions.
method Exploiting permutation-equivalence to refine confidence sets.
result Confidence sets shrink at asymptotic rates of O ( 1 / ∑ k ∈ K n k ) O(1/\sqrt{\sum_{k\in \mathcal K} n_k}) O ( 1/ ∑ k ∈ K n k ) and O ( 1 / max k ∈ K n k ) O(1/\max_{k\in K} n_{k}) O ( 1/ max k ∈ K n k ) . Prove non-asymptotic bounds for minimal risk in statistical learning
problem Estimating minimal risk in statistical learning
method Using concentration inequalities
result Non-asymptotic bounds for minimal risk
New tighter confidence bounds for sequential kernel regression.
problem Quantifying uncertainty in sequential learning algorithms.
method Martingale tail inequalities and conic programming.
result New confidence bounds are tighter than existing ones.
New method reduces variance in stochastic optimization with high confidence.
problem Achieving high-probability guarantees in stochastic optimization with weaker noise assumptions.
method Stochastic proximal point method combining proximal subproblem solver and probability booster.
result Demonstrates convergence with low sample complexity under bounded variance assumptions.
The SPS method constructs confidence regions for true parameters with optimal sample complexity.
problem Constructing exact, non-asymptotic confidence regions for true system parameters.
method Sign-Perturbed Sums (SPS) method, generalized to various types of problems.
result High probability upper bounds for SPS confidence regions show optimal shrinkage rate.
The study optimizes distribution estimation from samples with relative entropy error, adapting to sparse distributions.
problem Estimating discrete distributions with high-probability accuracy in relative entropy.
method Analysis of Laplace estimator and confidence-dependent smoothing techniques, including data-dependent smoothing.
result Optimal high-probability risk bounds for various estimators, including a new data-dependent smoothing method.
Proposes sparsified intervals for high-dimensional regression coefficients.
problem Challenges of high-dimensional regression coefficient inference.
method Sparsified simultaneous confidence intervals.
result Intervals can shrink some coefficients to zero, indicating unimportance.
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only limited results on the distribution of this error. We prove tight high-probabil…
Method estimates treatment effect bounds in sample selection models.
problem Estimating heterogeneous treatment effects in presence of sample selection.
method Debiased/double machine learning approach for non-linear and high-dimensional confounders.
result Substantially tighter effect bounds for younger users.
We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a …
Data-driven method for error estimation without needing class complexity.
problem Constructing confidence intervals for a class of estimates.
method Data-driven approach to derive high-probability upper bounds on maximum error.
result Method naturally adapts to unknown correlation structures and works for finite and infinite classes.
Study improves model fit by transferring info from related datasets.
problem Improving model fit on target data using source data.
method Proposes a transfer learning algorithm for GLMs, derives error bounds, and introduces detection of informative sources.
result Theoretical and practical improvements over classical methods in high-dimensional GLM settings.
New algorithms improve stopping time for best arm identification.
problem Efficiently identifying the best alternative in experiments.
method Proposed algorithms with exponential-tailed stopping time.
result Proved that some algorithms never stop, leading to new methods.
The paper relaxes the stability condition to boost confidence in generalization for randomized learning algorithms.
problem The tension between uniform stability and L 2 L_2 L 2 -stability in generalization bounds. method Establishes in-expectation first moment generalization error bounds for L 2 L_2 L 2 -stable randomized learning algorithms and uses subbagging to achieve near-tight exponential bounds. result Improves generalization bounds for convex and non-convex optimization problems with SGD.
Study contextual bandits with stage-wise constraints, proving regret bounds and extending results.
problem Contextual bandits with stage-wise constraints in high probability and expectation settings.
method Upper-confidence bound algorithms for linear and non-linear reward/cost functions, extending to multiple constraints.
result Regret bounds for various settings, including non-linear reward/cost functions.
The paper studies privacy-protected BAI with fixed confidence, deriving lower bounds and proposing an adaptive algorithm.
problem Privacy-protected Best Arm Identification (BAI) in data-sensitive applications.
method Derives lower bounds on sample complexity, proposes AdaP-TT algorithm with Laplace noise, and validates with experiments.
result AdaP-TT matches the sample complexity lower bound up to constants in the high-privacy regime.
Develops a method to find costly high-confidence errors in black box models.
problem Finding rare high-confidence errors missed by random sampling.
method Adversarial perturbation-guided search technique to find errors at rates greater than expected given model confidence.
result Our Adversarial Distance search discovers high-confidence errors at a rate greater than expected given model confidence.
A new differentiable UCB algorithm for linear bandits learns adaptive confidence bounds.
problem Inability of UCB to strike optimal exploration-exploitation due to confidence bounds.
method Proposes a differentiable linear bandit algorithm and a gradient estimator for learning adaptive confidence bounds.
result Achieves a i l d e O ( β ^ d T ) ilde{\mathcal{O}}(\hatβ\sqrt{dT}) i l d e O ( β ^ d T ) upper bound of T T T -round regret. 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.
Algorithm finds small confidence sets for arbitrary distributions.
problem Learning high-density regions in arbitrary distributions.
method Competitive with sets from a concept class with bounded VC-dimension.
result Algorithm finds a confidence set with volume exp ( i l d e O ( d 1 / 2 ) ) \exp( ilde{O}(d^{1/2})) exp ( i l d e O ( d 1/2 )) competitive with optimal ball. New method predicts sets under unknown covariate shift with high confidence.
problem Adapting to unknown covariate shift in prediction sets.
method PredSet-1Step, a flexible distribution-free method.
result Achieves asymptotic probably approximately correct coverage.
New method constructs confidence sets for GLMs via game theory.
problem Developing reliable confidence intervals for GLM parameters.
method Reduction to sequential prediction games with low regret.
result Online-to-confidence-set conversions provide new types of intervals.
The paper develops a method to create non-asymptotic confidence ellipsoids for linear regression without strong noise distribution assumptions.
problem Constructing reliable confidence regions for linear regression with finite sample sizes and general noise distributions.
method The paper introduces the SPS EOA algorithm to create non-asymptotically guaranteed confidence ellipsoids for linear regression problems.
result The sizes of SPS outer ellipsoids are shown to decrease at the optimal rate for linear regression problems.
We develop an efficient algorithm to find confidence ellipsoids with volume guarantees in high dimensions.
problem Finding robust confidence ellipsoids in high-dimensional data.
method Polynomial time algorithm using primal-dual structure and geometric Brascamp-Lieb inequality.
result Algorithm finds ellipsoids within a O ( β ) γ d O(β)^{γd} O ( β ) γ d volume factor of best β β β -conditioned ellipsoid. Develops methods for estimating and providing confidence bands in sparse high-dimensional additive models.
problem Estimating and providing reliable confidence bands for nonparametric components in high-dimensional additive models.
method Integrates sieve estimation into a high-dimensional Z-estimation framework, employing a multiplier bootstrap procedure.
result Constructs uniformly valid confidence bands for the target component f 1 f_1 f 1 in sparse high-dimensional additive models. Novel confidence intervals improve convergence rates for sparse kernel-based models.
problem High computational cost in kernel-based learning models.
method Novel confidence intervals for Nyström method and sparse variational Gaussian process approximation.
result Improved performance bounds in regression and optimization problems.
Designs adaptive controller for networked control systems with wireless data transmission.
problem Adaptive control in networked systems with unreliable wireless channels.
method Upper Confidence Bounds for Networked Control Systems (UCB-NCS) learning rule.
result Non-asymptotic performance guarantees with a regret bound of O(C√T).
Measuring mutual information from finite data is difficult. Recent work has considered variational methods maximizing a lower bound. In this paper, we prove that serious statistical limitations are inherent to any method of measuring mutual information. More specifically, we show that any distribution-free high-confide…
The paper introduces methods to quantify uncertainty in sampling without replacement.
problem Accurately estimating parameters from finite populations sampled without replacement.
method Develops confidence sequences using Bayesian and empirical methods.
result Improved confidence intervals and sequences for sampling without replacement.
BALLET filters a high-confidence region of interest for Bayesian optimization.
problem High-dimensional and non-stationary Bayesian optimization challenges.
method Adaptive level-set estimation using two probabilistic models.
result Ballets can efficiently shrink the search space and exhibit tighter regret bounds.
The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
UCB-V algorithm improves on UCB for MAB problems with variance estimates.
problem Optimizing arm selection in MAB problems with variance information.
method Asymptotic and high probability analysis of UCB-V algorithm.
result UCB-V can exhibit instability in arm-pulling rates but achieves refined regret bounds.
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…
This paper analyzes the sample complexity of SPS method for scalar linear regression.
problem Analyzing the sample complexity of the Sign-Perturbed Sums (SPS) identification method.
method The paper provides high probability upper bounds for the sizes of SPS confidence intervals under different sets of assumptions.
result The sizes of SPS confidence intervals shrink at a geometric rate around the true parameter, if observation noises are subgaussian.