New aggregation strategy handles unbounded losses with regret bounds.
problem Online optimization with unbounded loss functions.
method Follow The Regularized Leader (FTRL) with φ-divergence.
result Worst regret bound for unbounded losses with alternative divergences.
The paper explores how regularization can lead to convergence in imperfect information games.
problem Finding equilibrium in imperfect information games with imperfect information.
method Investigates Follow the Regularized Leader dynamics and how adding a regularization term can lead to strong convergence guarantees.
result The approach leads to algorithms that converge exactly to the Nash equilibrium in imperfect information games.
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. Mutation improves FTRL convergence in zero-sum games.
problem Lack of last-iterate convergence in FTRL variants.
method Introduced mutation to perturb action probabilities in FTRL.
result M-FTRL converges to Nash equilibria under full-information feedback.
New algorithm expands FTRL framework with improved worst-case regret bounds.
problem Online learning with improved worst-case regret bounds.
method Generalized implicit Follow-The-Regularized-Leader (FTRL) algorithm.
result Unified framework for designing updates improving worst-case regret bounds.
Algorithm optimizes functions without parameters, converging to global minima.
problem Optimizing functions without parameters.
method Follow The Regularized Leader with rescaled gradients and time-varying regularizers.
result Converges to global minimizer for variationally coherent functions.
Develops a Best-of-Both-Worlds algorithm for linear contextual bandits with Tsallis entropy.
problem Linear contextual bandits with i.i.d. contexts.
method Follow-The-Regularized-Leader (FTRL) with Tsallis entropy.
result Achieves $O\left(\log(T)^{\frac{1+β}{2+β}}T^{\frac{1}{2+β}}
ight)$ regret under margin condition.
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.
Adaptive learning rate improves FTRL's performance in online learning.
problem Optimizing FTRL's learning rate for competitive regret in online learning.
method Formulated as a sequential decision-making problem, introduced competitive analysis framework, and proposed stability-penalty matching update rules.
result Achieved a constant competitive ratio under specific conditions, enabling Best-Of-Both-Worlds algorithms.
Paper proves suboptimal convergence rate of last iterate for SGDM.
problem Proves suboptimal convergence rate of last iterate for SGDM.
method Focuses on convergence rate of last iterate of SGDM, introduces Follow-The-Regularized-Leader-based algorithms.
result Shows optimal convergence rate of last iterate for unconstrained convex stochastic optimization problems.
We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the standard methods for minimizing the usual notion of regret fail, through our analysis …
The paper proposes a method to construct confidence sets using likelihood ratios for sequential decision-making.
problem Constructing valid uncertainty estimates for unknown quantities in sequential decision-making.
method The method uses likelihood ratios to create any-time valid confidence sequences without specialized treatment for each application.
result The proposed confidence sets maintain the prescribed coverage in a model-agnostic manner and their size depends on the choice of estimator sequence.
New algorithms reduce regret in both stochastic and adversarial partial monitoring problems.
problem Partial monitoring with k k k -actions and d d d -outcomes. method Follow-the-regularized-leader framework, exploration by optimization, adaptive learning rate.
result Best-of-both-worlds algorithms with favorable regret bounds in stochastic and adversarial settings.
New algorithms reduce regret in online MDPs by adapting to data and variance.
problem Adapting to both adversarial and stochastic environments in online MDPs.
method Develops algorithms based on global optimization and policy optimization, using optimistic follow-the-regularized-leader with log-barrier regularization.
result Achieves refined data-dependent and variance-dependent regret bounds.
Develops parameter-free online mirror descent for optimal dynamic regret.
problem Optimal online linear optimization in unbounded domains.
method Modified online mirror descent framework for parameter-free algorithms.
result First unconstrained online linear optimization achieving optimal dynamic regret.
Improved regret bound for adversarial MDPs with linear function approximation.
problem Learning in adversarial MDPs with changing loss functions and large state spaces.
method Two algorithms: refined FTRL with log-barrier regularizer and magnitude-reduced loss estimator.
result Achieved i l d e O ( K ) ilde{\mathcal O}(\sqrt K) i l d e O ( K ) regret, improving over i l d e O ( K 2 / 3 ) ilde{\mathcal O}(K^{2/3}) i l d e O ( K 2/3 ) . Paper optimizes multi-agent learning in Markov games with generative model.
problem Learning Nash or CCE equilibria in multi-agent Markov games.
method Develops \myalg~algorithm and adaptive sampling scheme using FTRL method.
result Minimax-optimal learning of CCE with minimal samples.
New learning dynamics achieve fast convergence in games without needing to know utility scales.
problem Fast convergence guarantees in learning games require prior knowledge of utility scales.
method Developed scale-free and scale-invariant learning dynamics using optimistic follow-the-regularized-leader with adaptive learning rates and clipping techniques.
result Achieved fast convergence rates to Nash and correlated equilibria without prior utility scale knowledge.
New algorithm optimizes multi-armed bandits with low computational cost.
problem Optimizing multi-armed bandits with low computational cost.
method Proposes a new FTPL algorithm with optimistic principle for ambiguity.
result Unified regret analysis and low computational costs.
New adaptive learning rate improves FTRL's adaptivity to sparsity, game-dependency, and best-of-both-worlds.
problem Improving adaptivity in sequential decision-making problems.
method Developed a stability-penalty-adaptive (SPA) learning rate for FTRL.
result First BOBW algorithm with sparsity-dependent bound.
The online problem of computing the top eigenvector is fundamental to machine learning. In both adversarial and stochastic settings, previous results (such as matrix multiplicative weight update, follow the regularized leader, follow the compressed leader, block power method) either achieve optimal regret but run slow,…
New bounds for online portfolio selection without smoothness assumptions.
problem Online portfolio selection with non-Lipschitz, non-smooth losses.
method Data-dependent bounds using novel smoothness characterizations and FTRL with self-concordant regularizers.
result Achieves logarithmic regrets when data is 'easy' and sublinear worst-case regrets.
Improved algorithm reduces regret in corrupted expert advice setting.
problem Prediction with expert advice in the presence of adversarial corruption.
method Multiplicative Weights algorithm with decreasing step sizes.
result Achieves constant regret and optimal performance in various environments.
New algorithm reduces regret in collaborative multi-agent bandit problems.
problem Optimizing decisions in a network of agents with communication delays.
method Follow-the-Regularized-Leader (FTRL) algorithm with suitable regularizers and communication protocols.
result Upper bound on individual regret matches lower bound up to a constant factor.
In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required Ω ( n 4 ) Ω(n^4) Ω ( n 4 ) running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time O ( n 2 + ε ) O(n^{2+\varepsilon}) O ( n 2 + ε ) . The funda…
New algorithm reduces regret and constraint violation in online convex optimization with predictions.
problem Online convex optimization with time-varying constraints and predictions.
method Primal-dual algorithm combining Follow-The-Regularized-Leader with adaptive steps.
result Achieves O ( T 3 − β 4 ) \mathcal O(T^{\frac{3-β}{4}}) O ( T 4 3 − β ) regret and O ( T 1 + β 2 ) \mathcal O(T^{\frac{1+β}{2}}) O ( T 2 1 + β ) constraint violation bounds. Unified algorithm for linear bandits with improved regret bound.
problem Adversarial linear bandits with improved regret.
method Self-concordant perturbations in FTPL framework.
result Regret bound of O ( d n ln n ) \mathcal{O}(d\sqrt{n \ln n}) O ( d n ln n ) for hypercube and ℓ 2 \ell_2 ℓ 2 ball. New study shows FTRL mechanism works with correlated events.
problem Forecasting competitions with correlated events.
method Introduces block correlation and uses FTRL mechanism.
result FTRL mechanism retains ε ε ε -optimal guarantee with O ( b 2 log ( n ) / ε 2 ) O(b^2 \log(n)/ε^2) O ( b 2 log ( n ) / ε 2 ) events for correlated events. New algorithm for online optimization over symmetric cones, unifying previous methods.
problem Online convex optimization over symmetric cones.
method Symmetric-Cone Multiplicative Weights Update (SCMWU) algorithm.
result SCMWU is a no-regret algorithm.
Study learns optimal strategies in imperfect information games with self-play.
problem Learning optimal strategies in imperfect information games.
method Proposes Follow the Regularized Leader (FTRL) algorithms for imperfect information games.
result Proposes two FTRL algorithms: Balanced FTRL and Adaptive FTRL.
Study on online regression with noise, achieving near-optimal regret bounds.
problem Online generalized linear regression with stochastic noise.
method Sharp analysis of FTRL algorithm for stochastic label noise.
result Achieved near-optimal regret bounds for O ( σ 2 d log T ) + o ( log T ) O(σ^2 d \log T) + o(\log T) O ( σ 2 d log T ) + o ( log T ) . New algorithm reduces regret in both adversarial and stochastic contexts.
problem Contextual combinatorial semi-bandits with adversarial and corrupted stochastic regimes.
method Follow-the-Regularized-Leader (FTRL) framework with Shannon entropy regularizer, accelerated by Karush-Kuhn-Tucker conditions.
result Achieves O ~ ( T ) \widetilde{\mathcal{O}}(\sqrt{T}) O ( T ) regret in adversarial and O ~ ( ln T ) \widetilde{\mathcal{O}}(\ln T) O ( ln T ) regret in corrupted stochastic regimes. New algorithm achieves best-of-both-worlds performance in various online learning settings.
problem Achieving optimal performance in both adversarial and stochastic online learning settings.
method General reduction from best-of-both worlds to FTRL and OMD algorithms.
result Transformed existing algorithms into new ones with best-of-both-worlds guarantees.
Algorithm learns both stochastic and adversarial MDPs with best-of-both-worlds guarantees.
problem Learning episodic MDPs with known transition and bandit feedback.
method Follow-the-Regularized-Leader method with a hybrid regularizer.
result Achieves O ( l o g T ) \mathcal{O}(log T) O ( l o g T ) regret for stochastic losses and i l d e O ( T ) ilde{\mathcal{O}}(\sqrt{T}) i l d e O ( T ) regret for adversarial losses. Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.
problem Learning dynamics in bilinear saddle-point problems with bandit feedback.
method Uncoupled learning algorithm combining experimental design and FTRL with a tailored regularizer.
result Last-iterate convergence rate of i l d e O ( T − 1 / 4 ) ilde{O}(T^{-1/4}) i l d e O ( T − 1/4 ) in high probability. In this book, I introduce the concepts of online learning through a modern view based on convex optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I attempted to unify all the literature as instantiations of Online Mirror Descent and Follow-the-Regularized-L…
New algorithm reduces regret in online portfolio and quantum state learning.
problem Efficiently learning portfolios and quantum states online with minimal regret.
method BISONS algorithm for online portfolio selection, SCHRODINGER'S BISONS for quantum states, with polylogarithmic regret.
result First efficient algorithm with polylogarithmic regret for online portfolio selection and quantum states.
GALA adapts learning rates online by aligning gradients, improving deep learning model performance.
problem Fine-tuning learning rates for deep learning models requires extensive grid search.
method GALA dynamically adjusts learning rates by tracking gradient alignment and local curvature.
result GALA produces a flexible, adaptive learning rate schedule that increases when gradients align.
We propose a new algorithm for adversarial multi-armed bandits with unrestricted delays. The algorithm is based on a novel hybrid regularizer applied in the Follow the Regularized Leader (FTRL) framework. It achieves O ( k n + D log ( k ) ) \mathcal{O}(\sqrt{kn}+\sqrt{D\log(k)}) O ( k n + D log ( k ) ) regret guarantee, where k k k is the number of arms, n n n is the …
Recently, much work has been done on extending the scope of online learning and incremental stochastic optimization algorithms. In this paper we contribute to this effort in two ways: First, based on a new regret decomposition and a generalization of Bregman divergences, we provide a self-contained, modular analysis of…
Improved FTRL algorithm for multi-armed bandits with various regularizers and multiple optimal arms.
problem Designing adaptive multi-armed bandit algorithms that perform optimally in both stochastic and adversarial settings.
method Follow-the-Regularized-Leader (FTRL) algorithm with a broad family of regularizers and a new learning rate schedule.
result Uniqueness of optimal arm assumption is unnecessary for FTRL with a broad family of regularizers.
New algorithms minimize regret with global costs in online learning.
problem Minimizing regret in online learning with global costs.
method Extended FTRL algorithms for Blackwell's approachability.
result First bounds on regret minimization with explicit dependence in p p p and d d d . New algorithm achieves data-dependent regret bounds in MDPs with unknown transitions.
problem Achieving best-of-both-worlds guarantees with data-dependent regret bounds in MDPs with unknown transitions.
method Optimistic follow-the-regularized-leader algorithm with new optimistic Q-function estimators and transition bonus.
result First-order, second-order, and path-length bounds with polylog(T) regret in the stochastic regime.
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.
This paper considers online convex optimization (OCO) problems - the paramount framework for online learning algorithm design. The loss function of learning task in OCO setting is based on streaming data so that OCO is a powerful tool to model large scale applications such as online recommender systems. Meanwhile, real…
FTPL with Fréchet perturbation achieves near optimal regret bounds for m-set semi-bandit problems.
problem Optimizing regret bounds for m-set semi-bandit problems in adversarial and stochastic settings.
method Follow-the-Perturbed-Leader (FTPL) with Fréchet perturbation.
result Achieves near optimal regret bounds of O ( n m ( d log ( d ) + m 5 / 6 ) ) \mathcal{O}(\sqrt{nm}(\sqrt{d\log(d)}+m^{5/6})) O ( nm ( d log ( d ) + m 5/6 )) in adversarial setting and logarithmic regret in stochastic setting. This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning algorithm is if it is allowed a one-step look-ahead into the future. We show that given…
Adaptive learning rates improve FTPL's BOBW guarantees in bandit problems.
problem Improving Follow-the-Perturbed-Leader's BOBW guarantees in bandit problems.
method Introducing surrogate probability functions to compute adaptive learning rates without exact probabilities.
result BOBW guarantees for FTPL with Pareto perturbations for any α > 1 α>1 α > 1 .