The study classifies and characterizes totally symmetric sets in the general linear group.
problem Understanding the structure and properties of totally symmetric sets in the general linear group.
method Formulated a notion of irreducibility for totally symmetric sets in the general linear group and classified them.
result Classification of irreducible totally symmetric sets and those of maximal cardinality.
New method for linear bandits with unknown sparsity, improving sparse regret bounds.
problem Sparse regret bounds for unknown sparsity and adversarial action sets.
method Combines online to confidence set conversions with randomized model selection over nested confidence sets.
result First sparse regret bounds for unknown sparsity and adversarial action sets.
New method optimizes offline linear bandits using different confidence sets.
problem Optimizing offline learning for linear contextual bandits.
method Introduces a family of pessimistic learning rules based on ℓ p \ell_p ℓ p confidence sets. result The π ^ ∞ \hatπ_\infty π ^ ∞ rule achieves minimax performance and strictly dominates other predictors. Study reward-free RL in non-linear settings, improving efficiency and removing assumptions.
problem Improving sample efficiency in reward-free reinforcement learning for non-linear function approximation.
method Proposed RFOLIVE algorithm for minimal structural assumptions, analyzed hardness results for reward-free and reward-aware exploration.
result Statistical efficiency and hardness results under various structural assumptions, no need for reachability or explorability assumptions.
Graph Neural Nets (GNNs) have received increasing attentions, partially due to their superior performance in many node and graph classification tasks. However, there is a lack of understanding on what they are learning and how sophisticated the learned graph functions are. In this work, we propose a dissection of GNNs …
Study on totally symmetric sets with group applications.
problem Understanding totally symmetric sets and their group applications.
method Survey of existing theory and applications to various groups.
result Exploration of totally symmetric sets in multiple group contexts.
Analyzes the complexity of linear hypothesis sets using Rademacher complexity.
problem Understanding the complexity of linear hypothesis sets for various norms.
method Tight analysis of empirical Rademacher complexity for linear hypothesis classes with bounded weights.
result Improved bounds on Rademacher complexity for linear hypothesis sets, matching or improving existing results.
The paper classifies involutions on S^4, proving linearities under certain conditions.
problem Classifying involutions on S^4 with specific fixed-point sets.
method Combining surgery theory, Schoenflies theorem, and equivariant topology.
result Linear involutions on S^4 with 1-dimensional fixed-point sets are proven.
New method for robust linear regression in nearly linear time.
problem High-dimensional robust linear regression with adversarial corruption.
method Proposes estimators for two settings with near linear time complexity.
result Achieves optimal sample complexities and recovery guarantees.
The paper strengthens a theorem on crossings under linear perturbations with Hausdorff measure estimates.
problem Understanding multiple-point crossings under linear perturbations.
method Establishes a transversality theorem with Hausdorff measure estimates for exceptional parameter sets.
result Explicit upper bounds on the Hausdorff dimension of the exceptional set.
New method reduces ensemble size for linear bandits, achieving near optimal regret.
problem Achieving near optimal regret in linear bandits with limited ensemble size.
method Ensemble sampling with a size of order d log T d \log T d log T for a d d d -dimensional stochastic linear bandit. result Regret is at most ( d log T ) 5 / 2 T (d \log T)^{5/2} \sqrt{T} ( d log T ) 5/2 T , improving over linear scaling with T T T . Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …
We show that fundamental learning tasks, such as finding an approximate linear separator or linear regression, require memory at least \emph{quadratic} in the dimension, in a natural streaming setting. This implies that such problems cannot be solved (at least in this setting) by scalable memory-efficient streaming alg…
A new framework for robust policy learning in MDPs with linear mixture dynamics.
problem Off-dynamics challenge in real-world decision-making problems.
method Linear mixture DRMDP framework, meta algorithm for robust policy learning.
result The new framework provides a more refined representation of uncertainties.
Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.
problem Set membership estimation for linear systems with disturbances bounded by convex sets.
method Adopted block-martingale small-ball condition and random perturbed control policies to establish convergence rates.
result Established convergence rates for disturbances bounded by general convex sets.
Reward-free RL in linear MDPs is as hard as reward-aware RL.
problem Reward-free RL in linear MDPs without access to the reward function during exploration.
method Developed a computationally efficient algorithm with sample complexity O ~ ( d 2 H 5 / ε 2 ) \widetilde{\mathcal{O}}(d^2 H^5/ε^2) O ( d 2 H 5 / ε 2 ) . result Achieved optimal d d d dependence in linear MDPs for reward-free RL, matching the reward-aware RL setting. LLT transforms time series features based on linear laws.
problem Classifying univariate and multivariate time series.
method Time-delay embedding, spectral decomposition, and feature transformation.
result Transformed features improve classification accuracy.
The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.
problem Equivariant neural networks on homogeneous spaces.
method Deriving generalized steerability constraints for non-linear equivariant layers.
result The universality of the derived construction for non-linear equivariant layers.
New algorithms minimize regret in multi-task and lifelong linear bandits with shared representation.
problem Minimizing regret in multi-task and lifelong linear bandits with shared representation.
method Novel algorithms using efficient estimator for low-rank linear feature extractor and novel analysis.
result Achieved regret bounds matching minimax lower bound up to logarithmic factors.
Optimal linear contracts are possible even with memory in Gaussian settings.
problem Can optimal dynamic contracts be linear when agents control memory processes?
method Developed a methodology for non-Markovian and non-semimartingale settings, showed linear contracts are optimal for one-dimensional models.
result Linear contracts are optimal for one-dimensional models with memory, and for radial effort cost functions in higher dimensions.
A new classifier uses linear programming to classify sets based on their covariance.
problem Classifying sets of observations as a whole, not individually.
method Proposes a new classifier, CLIPS, using linear programming for set classification.
result The CLIPS classifier performs better with multiple observations in a set.
Linear Q-learning converges to a bounded set without divergence.
problem Proving linear Q-learning does not diverge and converges to a bounded set.
method No modifications to the original linear Q-learning algorithm, no Bellman completeness or near-optimality assumptions, only an ε-softmax behavior policy with adaptive temperature.
result First L 2 L^2 L 2 convergence rate of linear Q-learning iterates to a bounded set. Improved RL algorithm with linear MDPs for offline learning with partial data coverage.
problem Efficient offline RL with linear MDPs under partial data coverage.
method Primal-dual algorithm with O ( ε − 2 ) O(ε^{-2}) O ( ε − 2 ) sample complexity. result First computationally efficient algorithm with O ( ε − 2 ) O(ε^{-2}) O ( ε − 2 ) sample complexity for offline RL with linear MDPs under partial data coverage. Policy gradient converges linearly with Hadamard parameterization in tabular settings.
problem Convergence of policy gradient methods under Hadamard parameterization.
method Studied convergence rate and established linear convergence after k 0 k_0 k 0 iterations. result Algorithm converges linearly with rate $O( rac{1}{k})$ and faster locally after k 0 k_0 k 0 . The geometry of conjugation is mapped within Euclidean isometry groups.
problem Understanding conjugacy classes and their transformations in Euclidean groups.
method Geometric description of conjugacy classes and sets of conjugating elements based on linearizations.
result The conjugacy classes and sets of conjugating elements are described by the move-set and fix-set of linearizations.
A new definition for vector fields extends the Jacobi set concept.
problem Describing interactions between vector fields on complex domains.
method Piecewise linear approach for simplicial complexes.
result Generalizes Jacobi set concept to vector fields.
Policy gradient methods achieve linear convergence in simple MDPs.
problem Analyzing convergence rates of policy gradient methods in finite MDPs.
method Connections with policy iteration to show linear convergence with large step-sizes.
result Policy gradient methods succeed with large step-sizes and achieve linear rate of convergence.
Two algorithms address limited adaptivity in generalized linear contextual bandits.
problem Limited adaptivity in generalized linear contextual bandits.
method Two algorithms, B-GLinCB and RS-GLinCB, designed for two settings of limited adaptivity.
result Achieved i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret in both settings. New algorithms for learning MDPs with linear approximations in infinite-horizon settings.
problem Learning infinite-horizon average-reward MDPs with linear function approximation.
method Optimism principle, adversarial linear bandits, Natural Policy Gradient.
result Efficient algorithms with optimal or near-optimal regret bounds.
We prove that if an analytic subset A A A of a linear metric space X X X is not contained in a σ Z ω σZ_ω σ Z ω -subset of X X X then for every Polish convex set K K K with dense affine hull in X X X the sum A + K A+K A + K is non-meager in X X X and the sets A + A + K A+A+K A + A + K and A − A + K A-A+K A − A + K have non-empty interior in the completion X ˉ \bar X X ˉ of X X X . This implies t…
PILOT is a fast algorithm for linear model trees that outperforms existing methods.
problem Fitting linear model trees to large datasets efficiently and accurately.
method Greedy training with L 2 L^2 L 2 boosting and model selection rule. result PILOT outperforms standard decision trees and other linear model trees on various datasets.
Paper presents a machine learning method to improve significance tests for misspecified linear models.
problem Misspecification of linear assumptions in social science models leads to inaccurate significance levels.
method Apply machine learning to fit ground truth function, calculate linear approximation, and adjust the estimator.
result The method significantly outperforms linear regression for non-linear ground truth functions.
Novel confidence sets improve linear bandit performance by adapting to unknown noise levels.
problem Adapting to unknown noise levels in sequential decision-making.
method Proposed semi-adaptive and variance-adaptive confidence sets.
result Improved regret bounds and better performance in Bayesian optimization tasks.
Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.
problem Nonconvex minimax problems with coupled linear constraints.
method Zeroth-order primal-dual alternating projected gradient (ZO-PDAPG) and zeroth-order regularized momentum primal-dual projected gradient (ZO-RMPDPG) algorithms.
result Iteration complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints.
Optimal algorithms identify non-dominated arms in multi-output linear bandit models.
problem Identifying the Pareto Set in multi-output linear bandit models.
method Design-based algorithms for Pareto Set Identification (PSI) in a structured multi-output linear bandit model.
result Nearly optimal guarantees in both fixed-budget and fixed-confidence settings.
This paper tackles efficient federated learning for generalized linear bandits.
problem Limited communication efficiency restricts existing federated learning solutions to linear models.
method Proposes a communication-efficient solution framework using online and offline regression.
result Proves sub-linear regret and communication cost for generalized linear bandits.
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is an iterative scheme born from the adaptation of proximal point algorithm to nois…
IDS algorithm optimizes sequential decisions in various monitoring settings.
problem Optimizing sequential decisions in complex monitoring scenarios.
method Information-directed sampling (IDS) algorithm for linear partial monitoring.
result IDS achieves nearly worst-case rate optimality in finite-action games.
Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or proximal gradient descent assume access to a linear or quadratic oracle on the …
Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of function approximation raises a fundamental set of challenges involving computational …
The study proves manifolds with specific curvature and volume properties always split off a line at infinity.
problem Understanding the geometry at infinity of manifolds with linear volume growth and nonnegative Ricci curvature.
method Analyzing properties of Busemann functions and constructing examples.
result Manifolds with the specified properties always split off a line at infinity, with bounded diameter of level sets of Busemann functions.
Randomized exploration in linear bandits achieves optimal regret bounds.
problem Optimizing exploration in high-dimensional linear bandit problems.
method Analysis of Thompson sampling without forced optimism.
result Randomized exploration algorithms achieve an O ( d n log ( n ) ) O(d\sqrt{n} \log(n)) O ( d n log ( n )) regret bound in smooth, strongly convex action spaces. The paper derives estimates for linear potentials and applies them to improve Hausdorff dimensions of singular sets in conformal geometry.
problem Estimating linear potentials and understanding their impact on singular sets in conformal geometry.
method Derives estimates for linear potentials and applies them to improve Hausdorff dimensions of singular sets.
result Improves the Hausdorff dimensions of singular sets in conformal geometry, achieving stronger results in dimension 4.
Algorithm finds optimal regularizers for online linear optimization.
problem Finding optimal regularizers to minimize regret in online linear optimization.
method Algorithm takes input sets and outputs an optimal regularizer for FTRL.
result Algorithm guarantees regret within a constant factor of the best possible learning algorithm.
Unified approach for non-stationary linear bandits with dynamic regret.
problem Non-stationary linear bandits with round-specific feasible actions and drifting reward models.
method Unified misspecification-reduction viewpoint, restarting algorithms with misspecification-dependent regret guarantees.
result Optimal \(T^{2/3}P_T^{1/3}\) dynamic-regret dependence for both linear bandits and contextual linear bandits.
New method calibrates probabilistic linear solver for online coverage guarantees.
problem Uncertainty in probabilistic linear solver solutions without coverage guarantees.
method Online conformal prediction-PLS (OCP-PLS) method to calibrate uncertainty thresholds.
result Validates online calibration of uncertainty thresholds via online conformal prediction.
New method solves linear inverse problems using diffusion models.
problem Linear inverse problems in various domains.
method Posterior sampling with latent diffusion models.
result Provable sample recovery in linear models, outperforming previous methods.
Study linear regression with missing or corrupted data, showing error bounds.
problem Linear regression under missing or corrupted data.
method Information-theoretic lower bounds and efficient algorithms.
result Error bounds match in missing and corruption settings.