New lower bounds for bilevel optimization with first-order oracles.
problem Complexity of bilevel optimization with first-order oracles.
method Development of hard instances and proof of lower bounds.
result Nontrivial lower bounds for first-order zero-respecting algorithms.
Study on gradient complexity of private optimization with private oracles.
problem Analyzing the efficiency of differentially private optimization algorithms.
method Lower bounds on the number of first-order oracle queries for private optimization.
result Lower bounds on the number of queries for private optimization algorithms, showing a dimension-dependent runtime penalty.
We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed …
We study reinforcement learning in non-episodic factored Markov decision processes (FMDPs). We propose two near-optimal and oracle-efficient algorithms for FMDPs. Assuming oracle access to an FMDP planner, they enjoy a Bayesian and a frequentist regret bound respectively, both of which reduce to the near-optimal bound …
Study exact partition recovery with same-cluster oracle, bounded error.
problem Exact recovery of partitions with same-cluster oracle in adversarial error.
method Novel connection to correlation clustering, Rényi-Ulam framework, upper and lower bounds, randomized algorithm analysis, adaptivity-query complexity study.
result Upper and lower bounds on worst-case query complexity, expected performance bounds of randomized algorithm.
New data-dependent priors improve PAC-Bayes bounds.
problem Improving PAC-Bayes bounds for nonconvex learning.
method Using data to learn a conditional expectation of the posterior, given a subset of training data.
result Data-dependent oracle priors lead to stronger PAC-Bayes bounds.
Oracle-efficient algorithms for online learning with smoothed and hint-adversaries.
problem Online learning with beyond worst-case adversaries.
method Oracle-efficient algorithms for two settings: smoothed analysis and K-hint transductive learning. result Oracle-efficient regret bounds for learning real-valued and binary-valued functions.
We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error that can be controlled through a batch size parameter. Our proposed oracles are appealing in several practical contexts, for instance, risk measure estimation from a batch of independent and identically di…
Lower bounds found for nonconvex-strongly-concave min-max optimization problems.
problem Finding stationary points in nonconvex-strongly-concave min-max optimization.
method Provided lower bounds for first-order oracle complexity.
result Lower bounds of Ω(√κε⁻²) for deterministic oracles and Ω(√κε⁻² + κ¹/₃ε⁻⁴) for stochastic oracles.
An algorithm learns from multiple models to match an oracle's risk.
problem Learning from multiple noisy models to estimate a target parameter.
method Elimination rounds algorithm for adaptive learning.
result Risk of weak-oracle learner matches that of an oracle in multiple source case.
New method defends deep nets against large perturbations perceptible to humans.
problem Vulnerability of deep nets to adversarial attacks with perceptible but not changing predictions.
method Oracle-Aligned Adversarial Training (OA-AT) to align network predictions with Oracle's.
result Achieves state-of-the-art performance at large perturbation bounds (L-inf of 16/255 on CIFAR-10).
New analysis shows Thompson Sampling can work with greedy approximations in combinatorial bandits.
problem Thompson Sampling's theoretical limits with greedy approximations in combinatorial semi-bandits.
method Study with greedy oracle, providing lower and upper bounds on regret.
result First theoretical results showing TS can work with greedy approximations, breaking misconceptions.
New study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.
problem The difficulty of sampling from heavy-tailed distributions using Gaussian versus stable oracles.
method Comparison of Gaussian and stable oracles for proximal samplers.
result Gaussian samplers have a fundamental barrier for high-accuracy guarantees in heavy-tailed sampling, while stable samplers excel.
New algorithms solve stochastic variational inequalities without bounded variance assumption.
problem Solving stochastic variational inequalities without bounded variance assumption.
method Developed algorithms for two classes of problems: monotone and structured nonmonotone VIs.
result Oracle complexity of O(ε^-4) for solving VIs with unbounded domains and possibly unbounded variance.
Study on tradeoffs between mistakes and ERM oracle calls in online and transductive learning.
problem Analyzing online and transductive learning with limited ERM and weak consistency oracle access.
method Proves lower bounds and upper bounds on mistakes and oracle calls, considering realizable and agnostic cases.
result Achieves optimal mistake bounds with weak consistency queries for certain concept classes.
Crowdsourcing is an effective tool for human-powered computation on many tasks challenging for computers. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of hyperplane binary labeling rules under the Dawid-Skene crowdsourcing model. The bounds can be appl…
Improved algorithm for contextual bandits with reduced regret.
problem Adversarial contextual bandits with i.i.d. contexts.
method Oracle-efficient relaxation with O(T32(Klog(∣Π∣))31) regret bound. result First to improve regret bound and match original bound for stochastic case.
Algorithm solves online binary classification and infinite games using ERM oracle.
problem Online learning and solving infinite games with computationally inefficient oracles.
method Proposes an algorithm relying solely on ERM oracle calls for online binary classification and nonparametric games.
result Achieves finite and sublinearly growing regret in various settings.
Study sets a nontrivial upper limit on return forecasting accuracy.
problem Establishing a practical upper limit for return forecasting accuracy.
method Defined a coin-flip oracle model to theoretically outperform practical models and used its RextOOS2 as an upper bound. result Theoretical upper bound on RextOOS2 is a quadratic function of directional accuracy. We study the problem of interactively learning a binary classifier using noisy labeling and pairwise comparison oracles, where the comparison oracle answers which one in the given two instances is more likely to be positive. Learning from such oracles has multiple applications where obtaining direct labels is harder bu…
New bound improves on weighted majority vote risk estimation.
problem Improving risk estimation for weighted majority vote.
method Novel Chebyshev-Cantelli inequality and PAC-Bayes-Bennett inequality.
result New bounds improve on existing methods.
Study improves CTS's approximation regret for combinatorial bandits.
problem Improving CTS's performance on non-exact oracles.
method Develops a new O(log(T)/Δ) upper bound for CTS under specific conditions. result First O(log(T)/Δ) approximation regret upper bound for CTS. New algorithm reduces online learning error for unknown feature distributions.
problem Oracle-efficient hybrid online learning with unknown feature and label distributions.
method Computational efficient online predictor using ERM oracle for finite-VC and fat-shattering classes.
result Oracle-efficient sublinear regret bounds for hybrid online learning with unknown feature generation.
New algorithm tackles smooth online learning with optimal regret.
problem Smoothed online learning with adversarial distributions.
method Oracle-efficient algorithms for nonparametric function classes.
result Oracle-efficient algorithms achieve optimal regret bounds.
We give nearly matching upper and lower bounds on the oracle complexity of finding ε-stationary points (∥∇F(x)∥≤ε) in stochastic convex optimization. We jointly analyze the oracle complexity in both the local stochastic oracle model and the global oracle (or, statistical learning) model. This allows u…
We provide tight upper and lower bounds on the complexity of minimizing the average of m convex functions using gradient and prox oracles of the component functions. We show a significant gap between the complexity of deterministic vs randomized optimization. For smooth functions, we show that accelerated gradient de…
Unified formulation bridges adversarial and nonstationary bandits.
problem Handling time-varying reward distributions in multi-armed bandit problems.
method Unified oracle that switches between adversarial and nonstationary bandit oracles based on window size.
result Optimal regret achieved with matching lower bound.
We consider online learning in an adversarial, non-convex setting under the assumption that the learner has an access to an offline optimization oracle. In the general setting of prediction with expert advice, Hazan et al. (2016) established that in the optimization-oracle model, online learning requires exponentially …
GPE algorithm optimizes nonparametric contextual bandits with efficient regret bounds.
problem Optimizing nonparametric contextual bandits with efficient regret bounds.
method Inspired by Policy Elimination, GPE uses oracle-efficient techniques for nonparametric classes with infinite VC-dimension.
result GPE is regret-optimal for policy classes with integrable entropy, and for larger entropy, it provides an ε-greedy algorithm with matching regret bounds. The paper analyzes the efficiency of gradient estimation methods in noisy function evaluations.
problem Estimating gradients of smooth functions using noisy function evaluations.
method Information-theoretic lower bounds and finite difference method analysis.
result The finite difference method is not minimax optimal, suggesting room for improvement in gradient estimation.
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of n individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for each individual component. For the strongly-convex case, we prove such an algorith…
Gradient descent is efficient for solving feasibility problems with minimal memory and queries.
problem Finding a point in a given set using a memory-constrained algorithm with a separation oracle.
method Oracle complexity lower bounds for gradient descent and other algorithms.
result Gradient descent is Pareto-optimal in the oracle complexity/memory tradeoff for feasibility problems.
We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in high-dimensional settings. Our attention is focused on the ranking problem that is popular in machine learning. It is related to guessing the ordering between objects on the basis of their observed predictors. We p…
Paper establishes tight lower bounds for minimizing certain smooth and convex functions.
problem Minimizing high-order Hölder smooth and uniformly convex functions.
method Analyzes two asymmetric cases of q>p+ν and q<p+ν using worst-case oracle complexities. result Establishes worst-case oracle complexities for reaching an ε-approximate solution.
Optimizes bilevel empirical risk minimization with improved oracle calls.
problem Optimizing bilevel empirical risk minimization problems.
method Proposes a bilevel extension of the SARAH algorithm.
result Demonstrates improved oracle calls to achieve stationarity.
Improved algorithm finds second-order stationary points in non-convex optimization.
problem Minimizing non-convex objectives while preserving training data privacy.
method SpiderBoost framework with two gradient oracles: precise and less precise.
result Improved rates for finding second-order stationary points.
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moment, we show that iteratively reweighted $\ell_1…
Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.
problem Approximating fixed-points of nonexpansive and contractive operators in normed finite-dimensional spaces.
method Stochastic Halpern iteration with minibatch, analyzing oracle complexity.
result Improved oracle complexity for nonexpansive operators, with a lower bound of Ω(ε−3). New algorithm for online omniprediction with strong guarantees for continuous hypothesis classes.
problem Online adversarial learning with continuous hypothesis classes.
method Developed an oracle-efficient online multicalibration algorithm for infinite benchmark classes.
result First efficient online omnipredictor with strong guarantees for Lipschitz convex loss functions.
Quantum oracles help identify counterfactuals better than classical ones.
problem Identifying unknown causal parameters in causal models.
method Using quantum oracles to query and identify all causal parameters and counterfactuals.
result Quantum oracles enable identification of all two-way joint counterfactuals and tighter bounds on higher-order counterfactuals.
Estimates heavy hitters in data streams with queries, balancing accuracy and efficiency.
problem Identifying elements with high probability in i.i.d. samples.
method Sequential estimation algorithms for two query models: index and pair queries.
result Upper and lower bounds on query complexity for different distributions and noise models.
Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.
problem Lower complexity bounds for finite-sum optimization problems with various component functions.
method Developed novel approach to construct hard instances and analyzed PIFO algorithms.
result Established lower complexity bounds for convex-concave and nonconvex-strongly-concave objectives.
We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. To address the challenges posed by this noise, we analyze Bayesian oracles given the observed noisy features. Our Bayesian analysis reveals that the optimal hypothesis can significantly deviate f…
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and statistics, gaining an understanding of these complexity-theoretic issues is importa…
Improved Frank-Wolfe algorithm for constrained convex optimization with nearest extreme point oracle.
problem Constrained smooth convex minimization with limited linear optimization oracle access.
method Frank-Wolfe algorithm with nearest extreme point oracle.
result Improved complexity bounds for specific feasible sets, including linear convergence for 0ext−−1 polytopes. New protocol identifies impossible edge orientations in causal graphs.
problem Causal-discovery algorithms cannot distinguish edge directions without assumptions.
method Discrete impossibility certificates and oracle queries.
result Upper bound of 1+K expert interactions for DAG recovery. CJE calibrates cheap LLM judges against an oracle, achieving high accuracy at a fraction of the cost.
problem Inexpensive LLM judges can produce biased rankings, leading to unreliable outcomes.
method CJE uses a small oracle to calibrate cheap scores, then evaluates at scale with valid uncertainty.
result CJE achieves 99% pairwise ranking accuracy at 14x lower cost compared to a 16x oracle/judge cost ratio.
This paper tackles bandit optimization with a new pairwise comparison oracle for unknown strongly concave functions.
problem Maximizing an unknown strongly concave function over T periods with a biased pairwise comparison oracle.
method Introduced a discretization technique and local polynomial approximation to relate the problem to linear bandits. Developed a tournament successive elimination technique to localize the discretized cell and run LinUCB algorithm on cells.
result Established optimal regret bounds and improved state-of-the-art results in operations management problems.