SA algorithms control dynamic regret in non-stationary settings with strong convexity or exp-concavity.
problem Non-stationary Online Convex Optimization with dynamic regret control.
method Strongly Adaptive (SA) algorithms view dynamic regret as path variation of the comparator sequence.
result SA algorithms achieve i l d e O ( T V T ∨ log T ) ilde O(\sqrt{TV_T} \vee \log T) i l d e O ( T V T ∨ log T ) and i l d e O ( d T V T ∨ d log T ) ilde O(\sqrt{dTV_T} \vee d\log T) i l d e O ( d T V T ∨ d log T ) dynamic regret for strongly convex and exp-concave losses, respectively. New method reduces second-order KOCO complexity with adaptive sketching.
problem Efficiently solving kernel online convex optimization problems with strong curvature.
method Kernel Online Newton Step (KONS) with adaptive matrix sketching.
result Achieves O ( d e x t e f f log T ) \mathcal{O}(d_{ ext{eff}}\log T) O ( d e x t e f f log T ) regret with reduced space and time complexity. Stochastic gradient method stabilizes learning of approximated kernel functions.
problem Learning an approximated kernel function for binary classification.
method Stochastic gradient method applied to online convex optimization with random Fourier features.
result Stochastic gradient method is stable and generalizes well for approximated kernel functions under given assumptions.
A new BO method adapts hyperparameters online and uses a novel kernel for global and local optimization.
problem Expensive black-box optimization problems.
method Online length-scale adaption, mixed-global-local kernel, and adaptive hyperparameters.
result The proposed method outperforms state-of-the-art BO methods on global optimization benchmarks.
Online machine learns from signals robustly using consensus optimization.
problem Signal classification in online settings.
method Reproducing kernel Hilbert space with consensus optimization.
result Robust signal classification achieved.
Agents learn locally, converge globally in online learning with kernels.
problem Multi-agent learning with limited data and communication.
method Local regression functions with consensus constraints, functional stochastic gradient descent, and greedy subspace projections.
result Agents' functions converge to a neighborhood of the globally optimal one as the penalty parameter increases.
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.
IE-GP framework learns sequentially arriving data with adaptive kernels.
problem Sequential data adaptation in Gaussian process models.
method Incremental ensemble of Gaussian process learners with adaptive weights.
result IE-GP framework effectively learns and adapts to sequential data.
OBD algorithm optimizes online convex optimization with strong convexity and switching costs.
problem Online convex optimization with strong convexity and switching costs.
method Online Balanced Descent (OBD) algorithm for m m m -strongly convex costs with near-optimal dynamic regret and per-round accuracy for ε ε ε -smooth sequences. result OBD achieves a competitive ratio of 3 + O ( 1 / m ) 3 + O(1/m) 3 + O ( 1/ m ) for m m m -strongly convex costs. New algorithms robust to adversarial data achieve optimal performance.
problem Adversarial robustness in high-dimensional online learning problems.
method Alternating minimization scheme combining least-squares and convex reweighting.
result Achieves optimal robustness guarantees without distributional assumptions.
New approach for distributed online optimization of non-convex losses with sublinear regret.
problem Regret evaluation and consensus in distributed, multi-agent systems with non-convex losses.
method Composite regret metric and consensus-based online normalized gradient (CONGD) approach for pseudo-convex losses; offline optimization oracle for general non-convex losses.
result First sublinear regret bound for general distributed online non-convex learning.
New method optimizes on curved manifolds without curvature dependence.
problem Curvature-dependent regret in online optimization on Hadamard manifolds.
method Riemannian online gradient descent for h-convex functions.
result Established O ( T ) O(\sqrt{T}) O ( T ) and O ( log ( T ) ) O(\log(T)) O ( log ( T )) regret guarantees, curvature-independent. Universal algorithm for online convex optimization with optimal regret bounds.
problem Designing a universal algorithm for online convex optimization that works for multiple types of loss functions.
method Maler algorithm: runs multiple learning algorithms in parallel and selects the best one.
result Achieves optimal regret bounds for general convex, exponentially concave, and strongly convex functions.
Boosting improves online decision-making for large expert sets.
problem Online convex optimization with many experts is infeasible.
method Generalizes online boosting to online convex optimization and bandit linear optimization settings.
result Near-optimal regret guarantees for various feedback models.
Kernel interpolation speeds up online Gaussian process updates.
problem Efficiently updating Gaussian process posteriors with new data.
method Structured kernel interpolation for constant-time updates.
result Exact inference maintained with constant-time updates.
New algorithm SFHC achieves near-optimal costs with predictions for non-convex optimization.
problem Online optimization with non-convex hitting costs and movement costs.
method Synchronized Fixed Horizon Control (SFHC) algorithm with conditions on hitting and movement costs.
result Synchronized Fixed Horizon Control (SFHC) achieves a 1 + O ( 1 / w ) 1+O(1/w) 1 + O ( 1/ w ) competitive ratio for near-optimal costs. Optimal algorithms for online convex optimization with random order.
problem Online convex optimization with random order and non-convex loss functions.
method Stochastic gradient descent and algorithmic stability analysis.
result Achieves optimal bounds and significantly outperforms previous methods.
Two new online optimization algorithms tackle convex and submodular problems without projections or exact gradients.
problem Efficiently optimize non-convex functions like submodular functions under computational constraints.
method Meta-Frank-Wolfe and One-Shot Frank-Wolfe algorithms using stochastic gradient estimates.
result Achieve optimal adversarial regret bounds for convex and continuous submodular optimization.
Paper analyzes online Frank-Wolfe algorithms for convex and non-convex optimization with improved regret bounds.
problem Minimizing regret in online optimization with stochastic costs.
method Online variants of Frank-Wolfe algorithm with simple iterative updates and non-adaptive step size.
result Regret bounds and anytime optimality for convex and non-convex losses, with rates of O ( log 3 T / T ) {\cal O}( \log^3 T / T ) O ( log 3 T / T ) and O ( 1 / T ) {\cal O}(\sqrt{1/T}) O ( 1/ T ) , respectively. New control methods for systems with adversarial perturbations.
problem Control systems with adversarial noise.
method Online convex optimization and convex relaxations.
result Low regret policies against adversarial perturbations.
Optimized online learning with kernels for large-scale adversarial data.
problem Efficient online learning for large-scale, potentially adversarial datasets.
method Online variations of kernel Ridge regression using approximated basis functions.
result Optimal regret for a wide range of kernels with low per-round complexity.
New algorithms optimize non-smooth, non-convex objectives with improved complexity.
problem Optimizing non-smooth, non-convex stochastic objectives.
method Reduction to online learning, applying optimistic online learning techniques.
result Improved complexity for finding ( δ , ε ) (δ,ε) ( δ , ε ) -stationary points. Risk-averse approach for online convex bandit problems.
problem Online convex optimization with bandit feedback for risk-averse decision makers.
method Two algorithms: descent-type and ellipsoid method-based.
result Achieves optimal regret bounds for risk-aversion.
Optimizes particle filtering for non-stationary environments.
problem Tracking and adapting to non-stationary environments in online prediction.
method Formulated an efficient particle filtering method using online mirror descent algorithm.
result Achieves optimal particle efficiency in non-stationary environments.
Improved online learning for hidden-convex losses achieves optimal regret.
problem Adversarial online learning with nonconvex losses that become convex after reparameterization.
method Algorithmic equivalence between OGD and OMD on convex losses, with Hessian compatibility condition.
result OGD achieves O ( T ) \mathcal{O}(\sqrt{T}) O ( T ) regret for hidden-convex losses, matching optimal rate. We solve a complex optimization problem for Wasserstein barycenters using stochastic methods.
problem Optimizing the average of multiple probability distributions in a streaming data setting.
method We reformulate the problem as a convex-concave saddle-point problem and propose a stochastic optimization algorithm.
result Our algorithm has better complexity than existing methods for arbitrary distributions.
Reduces dynamic regret to static problem in RKHS.
problem Minimizing cumulative loss in online convex optimization.
method Reduces dynamic regret to static regret problem in RKHS.
result Optimal dynamic regret guarantees for linear losses and new bounds for exp-concave and improper linear regression.
New model shows online and statistical learning are computationally equivalent with optimization oracle.
problem Online learning in non-convex games with adversarial settings.
method Strengthening the oracle model to make online and statistical learning computationally equivalent.
result Efficient computation of non-convex game equilibria, including GANs, with optimization oracle.
Paper tackles online optimization with memory and competitive control.
problem Minimizing hitting and switching costs in online optimization problems.
method Optimistic Regularized Online Balanced Descent algorithm.
result Achieves a constant, dimension-free competitive ratio.
Optimal hidden-target learning for online inventory optimization on general convex sets.
problem Online inventory optimization (OIO) on arbitrary bounded convex capacity sets.
method Maintaining a hidden target and projecting it onto the feasible order-up-to set.
result The method improves the best known regret guarantee for OIO on general convex sets from inverse to inverse-square-root dependence on the common-demand probability.
New framework uses tempered optimism to handle imperfect experts in online learning.
problem Challenges of implicit optimism in practical online learning environments.
method Introduces tempered optimism as a framework for online non-convex learning, modifies existing algorithms.
result Demonstrates tempered optimism as a fruitful paradigm for online non-convex learning.
FTPL achieves optimal regret in online non-convex learning.
problem Online non-convex learning with non-convex losses.
method Follow the Perturbed Leader (FTPL) algorithm.
result FTPL achieves optimal regret rate of O ( T − 1 / 2 ) O(T^{-1/2}) O ( T − 1/2 ) . Optimal control in changing systems without strong convexity assumptions.
problem Adversarial changes in convex costs for unknown linear systems.
method Non-convex lower confidence bounds and computationally-efficient regret minimization.
result Achieves T \smash{\sqrt{T}} T -regret rate, optimal compared to best stabilizing controller. New algorithms achieve optimal performance in online convex optimization with strong convexity and squared ℓ 2 \ell_2 ℓ 2 norms.
problem Optimal performance in online convex optimization with specific cost structures.
method Proposed and analyzed new algorithms (G-OBD, R-OBD) with theoretical guarantees.
result G-OBD and R-OBD achieve optimal competitive ratios of O ( m − 1 / 2 ) O(m^{-1/2}) O ( m − 1/2 ) under specific conditions. Optimal online optimization algorithm without loss bounds.
problem Online convex optimization in unconstrained domains and losses.
method RescaledExp algorithm achieving optimal regret.
result RescaledExp matches lower bound asymptotically.
Paper tackles online convex optimization with stochastic constraints.
problem Online convex optimization with stochastic constraints.
method Proposes a new algorithm achieving O ( T ) O(\sqrt{T}) O ( T ) expected regret and constraint violations and O ( T log ( T ) ) O(\sqrt{T}\log(T)) O ( T log ( T )) high probability regret and constraint violations. result Achieves optimal regret and constraint violation bounds.
Pairwise learning usually refers to a learning task which involves a loss function depending on pairs of examples, among which most notable ones include ranking, metric learning and AUC maximization. In this paper, we study an online algorithm for pairwise learning with a least-square loss function in an unconstrained …
Extends boosting to multiclass online agnostic classification.
problem Online multiclass classification with weak learners.
method Reduces multiclass online agnostic boosting to online convex optimization.
result First boosting algorithm for online agnostic multiclass classification.
Optimal bounds on regret and constraint violation in adversarial COCO.
problem Minimizing regret and cumulative constraint violation in adversarial COCO.
method New surrogate loss function and Follow-the-Regularized-Leader/Online Gradient Descent.
result Achieved optimal O ( T ) O(\sqrt{T}) O ( T ) bounds on both regret and cumulative constraint violation. Study optimizes decisions in real-time using inexact simulation solutions.
problem Real-time decision-making in simulation optimization with inexact solutions.
method Optimize then predict (OTP) approach, analyzing bias and variance in simulation-optimization algorithms.
result Unified analysis framework for OTP, establishing convergence rates and optimal allocation of computational budget.
Unified framework for analyzing online convex optimization across various settings.
problem Analyzing online convex optimization in different settings and feedback types.
method Unified framework allowing systematic proposal and analysis of meta-algorithms.
result Comparable regret bounds for various feedback types and adversary types.
Boosts weak online learners to strong ones with sublinear regret.
problem Online learning agnostic setting without strong guarantees.
method Reduction to online convex optimization, boosting via marginally-better-than-trivial regret guarantees.
result First agnostic online boosting algorithm with sublinear regret.
Improved online convex optimization in high dimensions with OBD.
problem Online convex optimization with high-dimensional action spaces and penalty for changes.
method Online Balanced Descent (OBD) algorithm, projecting onto level sets to balance costs.
result First algorithm to achieve a dimension-free competitive ratio of 3 + O ( 1 / α ) 3 + O(1/α) 3 + O ( 1/ α ) for locally polyhedral costs. Algorithm minimizes SP-Regret for online saddle point problem and related knapsack optimization.
problem Online saddle point problem and related online convex optimization with knapsacks.
method Proposed algorithms achieving sublinear SP-Regret in various settings.
result Achieved sublinear SP-Regret bounds for different problem settings.
New algorithm learns optimal stepsizes for SGD in noisy non-convex optimization.
problem Finding optimal stepsize for SGD in noisy non-convex optimization.
method Surrogate losses cast problem into online convex optimization, using no-regret algorithms.
result Self-tuned SGD algorithm with adaptive convergence rates.
New algorithm for online learning in episodic MDPs with convex objectives.
problem Online episodic convex reinforcement learning.
method Online mirror descent algorithm with varying constraint sets and exploration bonus.
result Near-optimal regret bounds for online CURL without prior knowledge of transition function.
New algorithm for online optimization with long-term constraints.
problem Online convex optimization with long-term constraints.
method Adaptive online gradient descent algorithm with cumulative regret bounds.
result Achieves bounds of O(T^max{ β β β ,1-- β β β }) for loss and O(T^(1-- β β β /2)) for constraint violations. Efficiently tunes hyperparameters for online traffic time series prediction.
problem Online hyperparameter tuning for machine learning models in time series prediction.
method Online hyperparameter optimization algorithm for Kernel Ridge regression.
result Achieves better or similar prediction accuracy with significantly less computation time.