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…
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48 results for “oracle complexity”
We give nearly matching upper and lower bounds on the oracle complexity of finding -stationary points () 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…
Lower Complexity Bounds for Nonconvex-Strongly-Convex Bilevel Optimization with First-Order Oraclescs.LG
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.
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of "2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization" by V. Koltchinskii [arXiv:0708.0083]
Piecewise polynomial interpolation-based gradient descent reduces oracle complexity for smooth loss functions.
problem Optimizing empirical risk minimization loss functions
method Piecewise polynomial interpolation-based gradient descent
result Oracle complexity is reduced for smooth loss functions
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.
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 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.
We provide tight upper and lower bounds on the complexity of minimizing the average of 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…
We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding Lovász extensions and the squared Euclidean norm, leading to algorithms requiring …
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 polytopes.
New algorithm learns efficiently with a simple 'yes/no' oracle.
problem Can efficient learning be achieved with a simpler oracle than ERM?
method Developed an oracle that returns 'yes' or 'no' for realizable datasets.
result Learnability is possible with a polynomial price in VC dimension.
Semi-supervised active clustering (SSAC) utilizes the knowledge of a domain expert to cluster data points by interactively making pairwise "same-cluster" queries. However, it is impractical to ask human oracles to answer every pairwise query. In this paper, we study the influence of allowing "not-sure" answers from a w…
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.
New algorithms sample convex bodies using Markov chains and restricted Gaussian oracles.
problem Sampling uniformly from convex bodies efficiently.
method Markov chain Monte Carlo with proximal sampler and restricted Gaussian oracle.
result Efficient implementation of RGO for uniform sampling on convex bodies.
We note that known methods achieving the optimal oracle complexity for first order convex optimization require quadratic memory, and ask whether this is necessary, and more broadly seek to characterize the minimax number of first order queries required to optimize a convex Lipschitz function subject to a memory constra…
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.
Optimal Guarantees for Algorithmic Reproducibility and Gradient Complexity in Convex Optimizationcs.LG
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.
Develops accelerated methods for optimization using low-dimensional projected-gradient information.
problem Optimization with low-dimensional projected-gradient information and Nesterov acceleration.
method Randomized-subspace Nesterov accelerated gradient methods for smooth convex and strongly convex optimization.
result Established accelerated oracle-complexity guarantees and unified basis for comparing sketch families.
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.
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…
Information-theoretic lower bounds on the oracle complexity of stochastic convex optimizationstat.ML
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…
Paper addresses online alignment of large language models under uncertain preference feedback.
problem Online alignment of large language models with misspecified preference feedback.
method Formulates an oracle-robust objective as a worst-case optimization problem for log-linear policies, and develops projected stochastic composite updates.
result Shows that the robust objective admits an exact closed-form decomposition and achieves oracle complexity.
Improved sample complexity for target Q-learning in finite MDPs with generative oracle.
problem Sample complexity of target Q-learning in finite MDPs with a generative oracle.
method Analyzed target Q-learning algorithm in tabular case with a generative oracle, improved sample complexity.
result Improved sample complexity for target Q-learning in various scenarios.
We consider the problem of adaptively PAC-learning a probability distribution 's mode by querying an oracle for information about a sequence of i.i.d. samples generated from . We consider two different query models: (a) each query is an index for which the oracle reveals…
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.
Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of allowing "not-sure" answers from a weak oracle and propose an effective algorithm …
New algorithm reduces super-arm selection complexity exponentially.
problem Combinatorial multi-armed bandits with cardinality constraint.
method Combination of group-testing and quantized Thompson sampling.
result Achieves same regret order as state-of-the-art algorithms with perfect oracle, but with reduced complexity.
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 .
Average Oracle outperforms DCC+NLS in portfolio optimization.
problem Optimizing portfolio performance in volatile markets.
method Comparing the Average Oracle to various DCC+NLS variants.
result The Average Oracle consistently yields higher Sharpe ratios.
We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and require only poly-logarithmically many calls to the approximation oracle per it…
New oracle uses uncertainty for active classification with noisy feedback.
problem Improving query complexity in interactive binary classifier learning.
method Proposes a new pairwise comparison oracle that considers uncertainty and an adaptive labeling algorithm.
result Demonstrates improved performance and efficiency compared to existing methods.
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 …
New research shows fixed-budget best-arm identification cannot match static oracle performance.
problem Fixed-budget best-arm identification's performance limitations.
method Analysis of various adaptive and static algorithms for best-arm identification.
result For any algorithm, there exists at least one instance where the error decay rate is at most \((1 + \frac{\log(K)}{8})^{-1}\) times that of the static oracle.
New algorithm improves gradient-based ERM for smooth convex losses.
problem Empirical risk minimization of smooth, strongly convex loss functions.
method Iterative gradient-based method with local polynomial regression.
result Oracle complexity of for our algorithm.
Algorithm identifies nearest mode in noisy data.
problem Identifying the point with the minimum k-th nearest neighbor distance in unknown multivariate probability density.
method Sequential learning algorithm using noisy oracle queries to adaptively decide which points to query.
result Upper bounds on query complexity show significant improvement over baselines.
Quantum algorithms for multi-armed bandits are explored with limited reward access.
problem Exploring quantum speed-ups in multi-armed bandit problems with limited reward information.
method Introduced new bandit models and showed query complexity equivalence with classical algorithms.
result No quadratic speed-up is possible for multi-armed bandits with limited reward access.
Accelerating Quantum Reinforcement Learning with a Quantum Natural Policy Gradient Based Approachquant-ph
A quantum reinforcement learning algorithm reduces sample complexity.
problem Quantum reinforcement learning under model-free settings with quantum oracle access.
method Quantum Natural Policy Gradient (QNPG) algorithm replacing random sampling with deterministic gradient estimation.
result QNPG achieves a sample complexity of for queries to the quantum oracle, significantly improving classical lower bound.
We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard assumptions, and use both classical stochastic and SARAH estimators for approxima…
On Acceleration of Gradient-Based Empirical Risk Minimization using Local Polynomial Regressionmath.OC
Accelerates ERM problems with LPI-GD and improved oracle complexity.
problem Empirical Risk Minimization (ERM) problems with strong convexity and smoothness.
method Local Polynomial Interpolation-based Gradient Descent (LPI-GD) and accelerated methods.
result Oracle complexity improved to $ ilde{O}\left(\sqrtσ m^d \log(1/\varepsilon)
ight)$.
New method finds stationary points in bilevel optimization problems.
problem Solving nonconvex-strongly-convex bilevel optimization problems.
method Restarted Accelerated HyperGradient Descent (RAHGD) method.
result Achieves best-known theoretical guarantees for finding stationary points in bilevel optimization.
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 investigate the computational complexity of several basic linear algebra primitives, including largest eigenvector computation and linear regression, in the computational model that allows access to the data via a matrix-vector product oracle. We show that for polynomial accuracy, calls to the oracle are nece…
RPI combines imitation and reinforcement learning to improve policies efficiently.
problem High sample complexity in reinforcement learning.
method Active interleaving between imitation and reinforcement learning, using oracle queries for exploration.
result RPI outperforms existing methods across various domains.