Paper develops methods for non-quadratic loss low-rank matrix recovery.
problem Recovery of low-rank matrices with non-quadratic losses.
method Projected gradient method with a regularity projection oracle.
result Projected gradient method converges globally and linearly.
Paper tackles online learning on curved spaces without projections.
problem Online learning on Riemannian manifolds with computational constraints.
method Develops projection-free algorithms for geodesically convex optimization.
result Achieves sub-linear regret guarantees in online geodesically convex optimization.
We propose in this paper a general framework for deriving loss functions for structured prediction. In our framework, the user chooses a convex set including the output space and provides an oracle for projecting onto that set. Given that oracle, our framework automatically generates a corresponding convex and smooth l…
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.
Improved method reduces projection calls for nonsmooth convex optimization.
problem Optimizing nonsmooth convex functions with convex constraints.
method MOPES and MOLES methods combining Moreau-Yosida smoothing and accelerated first-order schemes.
result Achieves ε ε ε -suboptimality with significantly fewer projection calls. New algorithms optimize actions under time-varying constraints without projecting.
problem Optimizing actions under time-varying constraints without projecting.
method Projection-free algorithms using linear optimization oracle.
result Guaranteed i l d e O ( T 3 / 4 ) ilde{O}(T^{3/4}) i l d e O ( T 3/4 ) regret and O ( T 7 / 8 ) O(T^{7/8}) O ( T 7/8 ) constraints violation. 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.
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 O ~ ( ε − 2 ) \widetilde{O}(\varepsilon^{-2}) O ( ε − 2 ) oracle complexity. New algorithm solves complex optimization problems without needing projections.
problem Optimizing nested functions under convex constraints with noisy evaluations.
method Projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization.
result The algorithm achieves ε ε ε -stationary solutions with complexity bounds independent of ε ε ε and T T T . We revisit the challenge of designing online algorithms for the bandit convex optimization problem (BCO) which are also scalable to high dimensional problems. Hence, we consider algorithms that are \textit{projection-free}, i.e., based on the conditional gradient method whose only access to the feasible decision set, i…
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularize…
Paper proposes estimators for sparse PCA with oracle property.
problem Estimating sparse principal subspace in high-dimensional settings.
method Semidefinite relaxation with novel regularizations.
result One estimator achieves exact support recovery and statistical rate.
Study efficient algorithms for nonconvex optimization with state-dependent Markov data.
problem Stochastic optimization with Markovian data and state-dependent transition kernels.
method Projection-based and projection-free algorithms for constrained nonconvex problems.
result The number of oracle calls to achieve an ε ε ε -stationary point is O ( 1 / ε 2.5 ) \mathcal{O}(1/ε^{2.5}) O ( 1/ ε 2.5 ) . SFC aims to protect the Amazon with a digital currency and smart contracts.
problem Protecting the Amazon's ecosystem and ensuring resource credibility.
method Blockchain, digital contracts, smart contracts with oracles.
result Ensures credibility and security for financial resources invested in Amazon projects.
Study mini-batch SGD noise and its limits, proving complexity guarantees.
problem Analyzing the noise in mini-batch SGD and its impact on optimization.
method Examined the conditional covariance and diffusion limits of SGD under different sampling designs.
result Proved mean-square upper bounds and Fisher van Trees lower bounds for SGD, linking them to effective dimension and condition number.
In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate O ( 1 ε 2 ) O\left(\frac{1}{\varepsilon^2}\right) O ( ε 2 1 ) improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan an…
A new algorithm for solving constrained convex optimization problems efficiently.
problem Constrained convex optimization problems requiring high accuracy solutions.
method Second-Order Conditional Gradient Sliding (SOCGS) algorithm, using projection-free methods to solve quadratic subproblems inexactly.
result Converges quadratically in primal gap after a finite number of linearly convergent iterations.
New algorithm reduces adaptive regret without projections.
problem Computational expense of projections in online convex optimization.
method Lazy gradient-based algorithm with set-membership computations.
result Near-optimal adaptive regret bounds for general convex functions.
Develops a new fairness learning approach for multi-task regression models.
problem Fairness in multi-task regression models with biased datasets.
method Uses rank-based non-parametric independence test (Mann Whitney U statistic) and reformulates as non-convex optimization problem.
result Outperforms state-of-the-art methods on fairness metrics.
Zeroth-order optimization methods lack inherent privacy guarantees.
problem Ensuring differential privacy in zeroth-order optimization methods.
method Analyzing ZO-GD with and without random initialization for convex and strongly convex objectives.
result ZO-GD is not differentially private for strongly convex objectives and can have superlinear privacy loss.
Prior knowledge on properties of a target model often come as discrete or combinatorial descriptions. This work provides a unified computational framework for defining norms that promote such structures. More specifically, we develop associated tools for optimization involving such norms given only the orthogonal proje…
Local LMO optimizes constrained problems using local linear minimization.
problem Constrained optimization problems with complex feasible sets.
method Designs a new projection-free gradient method using local linear minimization.
result Transfers convergence rates of Projected Gradient Descent to the projection-free world.
Develops asymptotic theory for deep Cox models to enable valid inference.
problem Theoretical gaps in deep neural network estimators for Cox models.
method Asymptotic distribution theory linking in-sample optimization error to population risk.
result Pointwise and multivariate asymptotic normality for subsampled ensemble estimators.
New sampling methods for constrained and composite distributions.
problem Sampling from log-concave distributions with constraints and composite structures.
method Proximal sampler applied to lifted convex sets with separation and subgradient oracles.
result Practical and unbiased samplers for constrained and composite distributions.
A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.
problem Solving variational inequality problems with multiple functional constraints efficiently.
method Constrained Gradient Method (CGM) for Minty variational inequality problems.
result The Constrained Gradient Method achieves complexity similar to projection-based methods but with cheaper oracles.
New algorithms for multivariate RL improve decision-making in complex systems.
problem Complex multi-objective decision-making in reinforcement learning.
method Oracle-free and computationally-tractable algorithms for multivariate distributional RL.
result Convergence rates match scalar reward settings and provide insights into reward dimensionality.
New PG methods tackle nonconvex optimization with auto-conditioned stepsizes.
problem Optimizing nonconvex functions over convex sets.
method Auto-conditioned projected gradient (AC-PG) methods and stochastic variants.
result Achieved optimal iteration complexity for finding approximate stationary points.
New framework for decentralized optimization of upper-linearizable functions with improved regret and complexity.
problem Decentralized optimization of upper-linearizable functions with general constraints.
method Decentralized projection-free optimization with upper-linearizable function framework.
result Regret of O ( T 1 − θ / 2 ) O(T^{1-θ/2}) O ( T 1 − θ /2 ) with communication complexity of O ( T θ ) O(T^θ) O ( T θ ) and linear optimization calls of O ( T 2 θ ) O(T^{2θ}) O ( T 2 θ ) . Algorithm minimizes loss and constraint violations in online convex optimization with smooth penalties.
problem Minimizing loss and constraint violations in online convex optimization with smooth penalties.
method Projected gradient descent over a set around the current action.
result Both dynamic regret and constraint violation are bounded by the path-length.
Oracle-efficient algorithms reduce combinatorial semi-bandit regret to logarithmic time.
problem Scalability issue in combinatorial semi-bandit problems due to high combinatorial optimization costs.
method Oracle-efficient frameworks that minimize oracle queries while maintaining tight regret guarantees.
result Achieved i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret with O ( log log T ) O(\log\log T) O ( log log T ) oracle queries for worst-case linear rewards. A discrete diffusion model learns denoising, scoring, and bridging in different coordinates.
problem Understanding what a discrete diffusion model learns in different coordinate systems.
method Rigorous derivation of continuous-time Markov chain ELBO, Oracle Distance theorem, and exact coordinates for optimizer.
result The negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one.
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.
MAMBA learns policies competitive with multiple conflicting oracles.
problem Learning policies from multiple conflicting oracles in reinforcement learning.
method MAMBA uses a gradient estimator in the style of GAE to optimize policies, leveraging demonstrations from multiple weak oracles.
result MAMBA outperforms the state-of-the-art in learning policies competitive with multiple conflicting oracles.
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…
A desirable property of interpretable models is small size, so that they are easily understandable by humans. This leads to the following challenges: (a) small sizes typically imply diminished accuracy, and (b) bespoke levers provided by model families to restrict size, e.g., L1 regularization, might be insufficient to…
Max-min margin Markov networks improve consistency in structured prediction.
problem Statistical inconsistency in max-margin methods for structured prediction.
method Defining a max-min margin formulation to overcome statistical inconsistency.
result Proves consistency and provides an explicit algorithm with finite sample generalization bounds.
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.
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.
SoQal reduces oracle label requests in active learning by up to 35%.
problem Exploiting unlabelled data in healthcare requires costly oracle labeling.
method Dynamic questioning strategy to minimize oracle label requests.
result SoQal reduces oracle label requests by up to 35%.
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 …
New oracles improve stochastic optimization with noisy or biased measurements.
problem Optimizing functions with noisy or biased measurements.
method Introduced biased gradient oracles for stochastic optimization, analyzed RSG and SGD algorithms with these oracles.
result Derived non-asymptotic bounds for convergence rates of algorithms with biased gradient oracles.
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.
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.
FSPA bypasses eigenvalue estimation for quantum PCA, achieving optimal complexity and robustness.
problem Quantum PCA eigenvalue estimation is computationally expensive and prone to errors.
method Filtered Spectral Projection Algorithm (FSPA) that projects onto the dominant spectral subspace directly.
result FSPA achieves optimal complexity and robustness, outperforming classical methods.
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.
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.
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.
Deep Jump Gaussian Processes model high-dimensional piecewise functions.
problem Modeling high-dimensional piecewise continuous functions with limited accuracy.
method Integrates region-specific locally linear projections with Jump Gaussian Processes (JGP) to capture local low-dimensional subspace structures.
result DJGP achieves superior predictive accuracy and more reliable uncertainty quantification compared to existing methods.