New algorithms estimate matrix norms without matrix multiplication.
problem Estimating matrix norms efficiently in a matrix-free setting.
method Randomized algorithms based on Hutchinson's estimator modifications.
result Oracle complexity bounds for two-to-infinity and one-to-two norms.
Panoptic trades options without oracles on Ethereum.
problem Trading options without relying on oracles.
method Perpetual, trustless, instant-settlement protocol on Ethereum.
result Trustless, permissionless trading of options on Uniswap v3.
AdaPID optimizes diffusion-based samplers by dynamically adjusting schedules.
problem Optimizing the intermediate-time dynamics in diffusion-based samplers.
method Develops a time-varying stiffness schedule using Piece-Wise-Constant (PWC) parametrizations and a hierarchical refinement approach.
result QoS-driven PWC schedules consistently improve sampling fidelity and accuracy.
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 ) . 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 introduce an efficient algorithmic framework for model selection in online learning, also known as parameter-free online learning. Departing from previous work, which has focused on highly structured function classes such as nested balls in Hilbert space, we propose a generic meta-algorithm framework that achieves o…
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 . New method removes oracle and reduces memory usage for robust MDPs.
problem Applying robust MDPs in practice due to model estimation and oracle requirements.
method Transformed robust MDPs into an alternative form allowing stochastic gradient methods and model-free approach.
result Sample-efficient algorithm with lower storage requirement and no oracle.
Method discovers symmetries in data with neural networks.
problem Discovering symmetries in high-dimensional data.
method Fully connected neural networks trained with a loss function for symmetry.
result Generators for symmetries in latent space.
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. 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…
New algorithm learns POMDPs without computational oracles.
problem Learning near-optimal policies in POMDPs with computationally hard oracles.
method Quasipolynomial-time algorithm using barycentric spanners for policy covers.
result First oracle-free learning algorithm for observable POMDPs.
New model-free RL algorithm tackles robust average-reward problems with finite sample complexity analysis.
problem Long-term decision-making in environments with varying dynamics.
method Proposes Robust Halpern Iteration (RHI) algorithm based on a black-box sampling oracle and multi-level Monte-Carlo estimator.
result Achieves ε-optimal robust policy with sample complexity of O(1/ε^(2+o(1))) under generative model setting.
Oracle inequality for sparse neural nets adapts to unknown structure.
problem Sparse deep neural nets in nonparametric regression.
method Gibbs posterior distribution with Metropolis-adjusted Langevin algorithms and mixture of uniform priors.
result Oracle inequality showing adaptation to unknown regularity and structure, achieving minimax-optimal rate of convergence.
ConfHit provides valid guarantees for generative models without oracle access.
problem Reliable guarantees for novel candidate generation in generative models.
method Formalizes certification and refinement of generated sets, leveraging weighted exchangeability and density-ratio weighted conformal p-values.
result Consistently delivers valid coverage guarantees and compact certified sets across various generative tasks.
We present a novel framework of knowledge distillation that is capable of learning powerful and efficient student models from ensemble teacher networks. Our approach addresses the inherent model capacity issue between teacher and student and aims to maximize benefit from teacher models during distillation by reducing t…
Sparse-penalized deep neural networks improve performance in weakly dependent processes.
problem Nonparametric regression and classification under weak dependence.
method Sparse-penalized deep neural networks with oracle inequalities and convergence rates established.
result The proposed estimators outperform non-penalized ones in simulations.
A new method for faster optimization of noisy functions.
problem Optimizing noisy functions efficiently.
method A universal and adaptive second-order method for convex functions.
result Achieves O ( σ / T ) O(σ/ \sqrt{T}) O ( σ / T ) convergence for stochastic oracles and O ( 1 / T 3 ) O( 1 / T^3) O ( 1/ T 3 ) for deterministic oracles. 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).
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 i l d e O ( ε − 1.5 ) ilde{\mathcal{O}}(ε^{-1.5}) i l d e O ( ε − 1.5 ) for queries to the quantum oracle, significantly improving classical lower bound. Develops new methods to estimate treatment effects in survival data with competing risks.
problem Estimating treatment effects in survival data with competing risks.
method Censoring Unbiased Transformations (CUTs) for survival outcomes with and without competing risks.
result Consistent estimates of heterogeneous cumulative incidence effects and total effects using HTE learners.
We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the algorithm succeeds with respect to {\em any} distribution on the unit ball in n n n …
Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained quadratic subproblem at every iteration. We present the \emph{Second-Order Conditional G…
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.
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 ) Ω(\varepsilon^{-3}) Ω ( ε − 3 ) . A new test method improves goodness-of-fit tests for copulas.
problem Developing robust tests for copula goodness-of-fit.
method Binary Expansion Approximation of UniformiTY (BEAUTY) and Binary Expansion Adaptive Symmetry Test (BEAST).
result The BEAST method improves empirical power against various alternatives.
New trust matrix quantifies breakdowns in deep neural networks.
problem Understanding trust breakdowns in deep learning models.
method Introduces trust matrix and conditional trust densities to analyze deep neural networks.
result Trust matrices reveal areas needing improvement for deep neural networks.
Develops accelerated fixed-point methods with delayed oracles for scientific computing.
problem Approximating fixed points of nonexpansive operators.
method Combines Nesterov's acceleration and KM iteration with delayed inexact oracles.
result Establishes improved convergence rates for fixed-point approximation.
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…
Improved analysis and new algorithm for gradient-free optimization of smooth functions.
problem Minimization of highly smooth functions with noisy oracle information.
method Two zero-order projected gradient descent algorithms based on randomization over the ℓ 2 \ell_2 ℓ 2 and ℓ 1 \ell_1 ℓ 1 spheres, with improved analysis and theoretical guarantees. result Improved convergence rates and theoretical guarantees for various function classes.
The paper tackles deep learning from dependent data, achieving optimal performance.
problem Deep learning from strongly mixing observations, especially with regularization and optimality.
method Sparse-penalized regularization for deep neural networks, oracle inequality for expected excess risk.
result Deep neural network estimator achieves minimax optimal rate for nonparametric autoregression.
Model-free Reinforcement Learning (RL) algorithms such as Q-learning [Watkins, Dayan 92] have been widely used in practice and can achieve human level performance in applications such as video games [Mnih et al. 15]. Recently, equipped with the idea of optimism in the face of uncertainty, Q-learning algorithms [Jin, Al…
Efficiently certifies global robustness of large neural networks with probabilistic guarantees.
problem Certifying robustness of large neural networks in a scalable and efficient manner.
method Sampling an ε-net and invoking a local robustness oracle.
result Certifies a probabilistic relaxation of robustness efficiently and globally.
Paper proposes a new method to optimize deep neural networks with sparse regularization.
problem Difficulty in achieving optimal convergence rates for deep neural networks due to sparsity constraints.
method Introduces a novel penalized estimation method for sparse DNNs, resolving computational and theoretical issues.
result Establishes an oracle inequality for the excess risk of the proposed sparse-penalized DNN estimator and derives convergence rates.
New algorithm optimizes convex functions with noisy evaluations in one dimension.
problem Optimizing convex functions with noisy zero-order evaluations in one dimension.
method Proposed a computationally efficient algorithm achieving O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) convergence rate. result Achieved the optimal O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) convergence rate, closing the gap in one dimension. Minimax PAC bounds for learning in exogenous contextual MDPs
problem PAC learning in tabular discounted Markov decision processes with exogenous i.i.d. contexts
method Variance-reduced algorithm for policy evaluation, best-value estimation, and best-policy extraction
result Minimax optimal sample complexity
Novel oracle-type inequality for logistic loss in DNNs achieves sharp convergence rates.
problem Generalization analysis for binary classification with DNNs and logistic loss.
method Established an oracle-type inequality to handle the boundedness of the target function.
result Optimal convergence rates for fully connected ReLU DNN classifiers trained with logistic loss.
New stability bounds for GD in overparameterised shallow nets without NTK assumptions.
problem Generalisation and excess risk bounds for shallow neural networks.
method Oracle inequalities and stability analysis of GD without kernelisation.
result Oracle type bounds reveal GD's generalisation is controlled by an interpolating network with shortest GD path.
Active learning selects most informative unlabeled samples for labeling.
problem Efficiently label unlabeled data in applications with scarce labeled data.
method Formulated as open-set recognition, uses VNNs to identify uncertain samples.
result Achieved state-of-the-art results on MNIST, CIFAR-10, and CIFAR-100.
Representation learning systems typically rely on massive amounts of labeled data in order to be trained to high accuracy. Recently, high-dimensional parametric models like neural networks have succeeded in building rich representations using either compressive, reconstructive or supervised criteria. However, the seman…
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.
The paper addresses nonconvex penalized LAD estimation in partial linear models using DNNs.
problem Challenges in nonconvex penalized LAD estimation with DNNs in partial linear models.
method Parameterizes nonparametric term with DNNs, formulates penalized LAD problem, introduces proximal subgradient method.
result Establishes consistency, convergence rate, and asymptotic normality of the estimator.
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. UCRL-WVTR tackles long-term reinforcement learning with general approximations, achieving horizon-free and instance-dependent regret bounds.
problem Long-term reinforcement learning with general function approximations.
method UCRL-WVTR proposes a novel algorithm, UCRL-WVTR, with weighted value-targeted regression and a high-order moment estimator.
result Achieves horizon-free and instance-dependent regret bounds matching minimax lower bounds up to logarithmic factors.
Deep neural networks are optimal for dependent data using PAC-Bayes bounds.
problem Optimizing deep neural networks for dependent data.
method PAC-Bayes oracle inequalities and Bernstein inequality.
result Upper and lower bounds match, proving minimax optimality.
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.
Proposes a new method for completing swap cycles in decentralized exchanges.
problem Completing swap cycles in decentralized exchanges efficiently and without slippage.
method Introduces an asset matrix formulation to verify and complete CoW cycles using graph traversal and imbalance correction.
result Demonstrates efficient discovery and insertion of synthetic orders for atomic cycle closure.
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.