Paper proves linear convergence of SCMS algorithm for directional data.
problem Identifying density ridges in directional data.
method Generalized SCMS algorithm to directional data, derived from SCGA with adaptive step size.
result Linear convergence of the proposed directional SCMS algorithm.
Optimal algorithms for non-linear ridge bandits reduce burn-in cost.
problem Non-linear models introduce a burn-in period with fixed cost.
method Two-stage algorithm: find initial action, then treat locally linear.
result Two-stage algorithm is statistically optimal.
Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.
problem Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
method Near-optimal algorithms with optimal error guarantees, achieving sample complexity n = i l d e O ( d / ε 2 ) n = ilde{O}(d/ε^2) n = i l d e O ( d / ε 2 ) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and …
Safe algorithm for linear bandits with safety constraints, matching previous results.
problem Designing safe bandit algorithms with linear safety constraints.
method Linear Thompson Sampling with frequentist regret analysis.
result Frequentist regret of order O ( d 3 / 2 log 1 / 2 d ⋅ T 1 / 2 log 3 / 2 T ) \mathcal{O} (d^{3/2}\log^{1/2}d \cdot T^{1/2}\log^{3/2}T) O ( d 3/2 log 1/2 d ⋅ T 1/2 log 3/2 T ) . Study finds exact limits for sparse regression with fewer observations than usual.
problem Understanding sparse linear regression with sublinear sparsity.
method Adaptive interpolation method and modified AMP algorithm.
result Exact asymptotic expressions for mutual information and MMSE in sublinear sparsity.
Optimizes pure exploration in linear bandits with a new algorithm.
problem Best-arm identification in linear stochastic bandits.
method Developed the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits.
result Avoids the pitfall of a simple but difficult instance and bypasses the need to solve an optimal design problem.
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation algorithm. Using the probabilistic model, we derive a matrix factorisation algorithm …
New algorithm for linear bandits learns from feature feedback, reducing regret.
problem Linear bandit problem with feature feedback.
method Developed new theory and algorithms for linear bandits with feature feedback.
result Achieves regret scaling like k T k\sqrt{T} k T , improving over traditional linear bandits. Efficient algorithms for online multiclass linear classification with bandit feedback under linear separability conditions.
problem Efficient online multiclass linear classification with bandit feedback for separable data.
method Design of efficient algorithms based on kernel Perceptron for strong and weak linear separability conditions.
result Near-optimal mistake bounds of $O\left( K/γ^2
ight)$ for strong separability and min ( 2 O ~ ( K log 2 ( 1 / γ ) ) , 2 O ~ ( 1 / γ log K ) ) \min (2^{\widetilde{O}(K \log^2 (1/γ))}, 2^{\widetilde{O}(\sqrt{1/γ} \log K)}) min ( 2 O ( K l o g 2 ( 1/ γ )) , 2 O ( 1/ γ l o g K ) ) for weak separability. New algorithm reduces reinforcement learning regret to sqrt(d^3T).
problem Efficient reinforcement learning with generalized linear function approximation.
method Optimistic closure assumption for generalized linear functions.
result Proved regret bound of O(sqrt(d^3T)).
LinMED is a new linear bandit algorithm with near-optimal regret bound.
problem Optimizing decision-making in linear bandit problems with sub-Gaussian distributions.
method LinMED is a randomized linear bandit algorithm with closed-form arm sampling probabilities.
result LinMED achieves a near-optimal regret bound of d n d\sqrt{n} d n up to logarithmic factors. 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.
This work identifies eigenvalues of unknown linear dynamics without full system identification.
problem Identifying parameters of a linear dynamical system is challenging.
method Developed a computationally efficient algorithm to estimate eigenvalues of the state-transition matrix.
result The algorithm can efficiently cluster multi-dimensional time series with temporal offsets and varying lengths.
New algorithm minimizes regret in stochastic linear bandits with perturbed history.
problem Minimizing cumulative regret in stochastic linear bandits.
method Perturbed-history exploration in a linear bandit (LinPHE) algorithm.
result Achieves a O ( d n ) O(d \sqrt{n}) O ( d n ) gap-free bound on cumulative regret. Improved regret bound for linear ensemble sampling.
problem Closing the gap between theory and practice in linear ensemble sampling.
method General regret analysis framework for linear bandit algorithms, revealing a relationship with LinPHE.
result Achieves a frequentist regret bound of i l d e O ( d 3 / 2 T ) ilde{O}(d^{3/2}\sqrt{T}) i l d e O ( d 3/2 T ) for linear ensemble sampling. First robust bandit algorithm for contextual bandits with sub-linear regret.
problem Vulnerability of linear contextual bandit algorithms to adversarial attacks.
method Proposes a robust bandit algorithm for stochastic linear contextual bandits under fully adaptive and omniscient attacks.
result Sub-linear regret under various attacks without requiring attack information.
Characterizes problems solvable via linear convergence algorithms.
problem Optimization problems solvable with linear convergence.
method Riemannian gradient descent.
result Characterized problems solvable via linear convergence.
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.
FTRL algorithm with negative entropy regularizer achieves best-of-three-world results for linear bandits.
problem Designing an FTRL algorithm for linear bandits with optimal regret bounds.
method Follow-the-regularized-leader (FTRL) algorithm with negative entropy regularizer.
result Regret bounds achieve the same or nearly the same order as detect-switch type algorithm but with simpler design.
EM algorithm converges globally for two-component mixed linear regression.
problem Global convergence of EM algorithm for mixed linear regression.
method Developed new theoretical analysis for EM algorithm convergence in mixed linear regression.
result EM algorithm converges globally for two-component mixed linear regression.
New algorithm for nonnegative tensor completion with linear convergence rate.
problem Tensor completion without known optimal sample complexity rate.
method Integer optimization using a specific 0-1 polytope gauge norm.
result Achieves information-theoretic rate with linear convergence.
New scalable algorithm improves linear regression accuracy and efficiency.
problem Improving linear regression accuracy and efficiency for large datasets.
method Developed new theory to model significance and multicollinearity as constraints, scaling with n n n in the 10,000s. result Significantly improves accuracy, reduces false detection rate, and speeds up computation.
Unified analysis of reweighted least-squares algorithms for linear models.
problem Recovering unknown signals from linear measurements using reweighted least squares.
method Unified asymptotic analysis of IRLS, lin-RFM, and alternating minimization algorithms.
result The algorithms can achieve favorable performance in a few iterations with appropriate reweighting.
New algorithm for choosing top-K options efficiently with linear space and non-linear feedback.
problem Choosing the best K out of N options at each time instant with efficient trade-off between exploration and exploitation.
method CMAB-SM algorithm, divide-and-conquer strategy, linear space, non-linear feedback.
result Achieves a sub-linear regret bound of $O(K^{ rac{1}{2}}N^{ rac{1}{3}}T^{ rac{2}{3}})$ .
New algorithm for linear optimization with adaptive corruption.
problem Stochastic linear optimization under adversarial corruption.
method Algorithm uses Löwner-John's ellipsoid for exploration and divides time into epochs.
result Regret increases linearly with corruption amount.
New algorithm solves phase retrieval with adaptive stopping criteria.
problem Robust phase retrieval problem as nonsmooth, nonconvex optimization.
method Inexact proximal linear algorithm with adaptive stopping criteria.
result Proposed methods are more efficient than existing methods.
New algorithm for offline RL with linear approx in MDPs and MGs, nearly optimal.
problem Offline RL with linear function approximation in MDPs and MGs.
method Pessimism-based algorithm with uncertainty decomposition via reference function.
result Nearly minimax optimal performance in offline RL for MDPs and MGs.
Study differential privacy in contextual linear bandits.
problem Maximizing rewards in a contextual bandit problem with private data.
method Adopted joint differential privacy, converted classic linear-UCB to joint-differentially private algorithm.
result First lower bound on additional regret for private algorithms.
New RL algorithm tackles nonstationary MDPs with linear approximations and varying rewards.
problem Nonstationary reinforcement learning with evolving reward and state transition functions.
method Developed a new algorithm LSVI-UCB-Restart with periodic restart, and parameter-free Ada-LSVI-UCB-Restart for unknown variation budgets.
result First minimax dynamic regret lower bound for nonstationary linear MDPs and linear MDPs lower bound.
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. 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 algorithm for identifying best arm in stochastic linear bandits with fixed confidence.
problem Identifying the best arm in stochastic linear bandits with fixed confidence.
method Extending an algorithm designed for Best Arm Identification to the ε ε ε -Thresholding Bandit Problem (TBP). result Asymptotically optimal algorithm for TBP.
Paper solves stochastic contextual linear bandits using linear bandit algorithms.
problem Stochastic contextual linear bandits with unknown context distribution.
method Establishes a reduction framework to convert to linear bandit problems.
result Achieves nearly optimal regret bound of O ( d T log T ) O(d\sqrt{T\log T}) O ( d T log T ) . Paper proposes a privacy-preserving RL algorithm for linear MDPs with theoretical guarantees.
problem Protecting users' private data in personalized services using RL.
method Local differential privacy (LDP) for RL with linear function approximation.
result Achieves a regret bound of $O(d^{5/4}H^{7/4}T^{3/4}\left(\log(1/δ)
ight)^{1/4}\sqrt{1/\varepsilon})$ for linear mixture MDPs.
DualIV simplifies non-linear IV regression via dual formulation.
problem Non-linear instrumental variable regression with potential first-stage regression bottleneck.
method Dual formulation of non-linear IV regression as a convex-concave saddle-point problem, leading to a kernel-based algorithm with analytic solution.
result Empirical results show competitive performance compared to existing algorithms.
New linear algorithms improve ICA over finite fields with lower bounds.
problem Linear Independent Component Analysis over finite fields.
method Greedy algorithm and sub-optimal variant.
result Our algorithms outperform existing methods and reduce overhead as scale increases.
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.
FSQ algorithm extends Q-learning to continuous actions with linear complexity.
problem Extending Q-learning to continuous action spaces with linear complexity.
method Discretization of the action space to maintain linear complexity.
result FSQ algorithm achieves linear complexity in the discretized problem.
New algorithm learns linear dynamical systems from measurements.
problem Learning system dynamics from linear measurements efficiently and accurately.
method Method of moments estimator to directly estimate Markov parameters.
result First polynomial time algorithm for learning linear dynamical systems.
New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.
problem RL with linear function approximation lacks uniform-PAC guarantees.
method FLUTE algorithm with minimax value function estimator and multi-level partition scheme.
result Uniform-PAC convergence to optimal policy with high probability.
Polynomial-time RL algorithm for constant actions under linear Bellman completeness.
problem Efficient online reinforcement learning with few actions.
method Polynomial-time algorithm based on linear function approximation.
result First computationally efficient algorithm for RL with constant actions under linear Bellman completeness.
Robust learning mixtures of linear regressions improve robustness.
problem Improving robustness in learning mixtures of linear regressions.
method Connecting mixtures of linear regressions and mixtures of Gaussians with thresholding for a quasi-polynomial time algorithm.
result The algorithm has significantly better robustness than previous results.
Proposes a new algorithm for non-stationary bandits.
problem Non-stationary reward distributions in contextual bandits.
method Multiscale changepoint detection for adaptive learning.
result Regret bound analysis and superior performance in experiments.
New algorithms solve linear bandits in high dimensions efficiently.
problem Maximizing bilinear functions over convex sets and ellipsoids.
method Two novel algorithms for solving the problem efficiently.
result First known method to implement optimistic algorithms for linear bandits in high dimensions.
New classifier combines locally linear kernels for fast and accurate non-linear classification.
problem Developing a fast and accurate non-linear classifier.
method Combines locally linear classifiers using a ℓ 1 \ell_1 ℓ 1 Multiple Kernel Learning (MKL) problem with scalable MKL training for streaming kernels. result The resulting classifier achieves high accuracy with fast inference time.
Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
New machine learning method solves semi-linear PDEs more accurately.
problem Solving semi-linear partial differential equations (PDEs)
method Improves existing machine learning algorithms using neural networks and deep learning techniques.
result New algorithm outperforms existing methods in accuracy.