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. New algorithm tackles smooth online learning with optimal regret.
problem Smoothed online learning with adversarial distributions.
method Oracle-efficient algorithms for nonparametric function classes.
result Oracle-efficient algorithms achieve optimal regret bounds.
Improved online classification with accurate predictions.
problem Online classification challenges with limited data.
method Designing an online learner that uses predictions to reduce regret.
result Expected regret is better than worst-case analysis, especially with accurate predictions.
OSGM uses online learning to adapt stepsize for faster convergence.
problem Improving convergence rates of first-order methods.
method OSGM combines online learning and feedback functions to adjust stepsize.
result OSGM achieves convergence rates asymptotically no worse than optimal.
Efficiently estimates online variational learning using importance sampling.
problem Online variational estimation in state-space models.
method Variational approach with Monte Carlo importance sampling.
result Proposed efficient algorithm for streaming data.
A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with individual guarantees. We close this gap by introducing a black-box modification to …
Oracle-efficient algorithms for online learning with smoothed and hint-adversaries.
problem Online learning with beyond worst-case adversaries.
method Oracle-efficient algorithms for two settings: smoothed analysis and K K K -hint transductive learning. result Oracle-efficient regret bounds for learning real-valued and binary-valued functions.
New methods improve online matrix optimization with reduced computational cost.
problem Online matrix optimization with operator norm constraints.
method Gradient-based prediction scheme with smoothed potentials for nuclear norm.
result Adaptive matrix optimizers match Shampoo's regret up to a constant factor.
The paper improves smoothed analysis for online problems with adaptive adversaries.
problem Online prediction, discrepancy minimization, and online optimization with adaptive adversaries.
method General technique to prove smoothed guarantees against adaptive adversaries, reducing to simpler oblivious adversaries.
result Strong smoothed guarantees for three online problems, matching or improving previous results.
New algorithm reduces prediction error in online learning without knowing base measure.
problem Smoothed online learning without knowledge of base measure.
method R-Cover algorithm based on recursive coverings.
result First algorithm to guarantee sublinear regret for agnostic smoothed online learning without prior knowledge of base measure.
The study bounds errors in learning smooth functions online.
problem Investigating worst-case error bounds for online learning of smooth functions.
method Analyzing the class of absolutely continuous functions with smoothness constraints and proving bounds on prediction errors.
result Proved bounds on the sum of the p e x t t h p^{ ext{th}} p e x t t h powers of absolute prediction errors for any number of trials. New algorithms achieve better regret bounds for online classification with relaxed benchmarks.
problem Competing with worst-case optimal binary loss in online classification.
method Comparing against predictors robust to small input perturbations, performing well under Gaussian smoothing, or maintaining a prescribed output margin.
result Regret guarantees depend only on VC dimension and instance space complexity, with an O ( log ( 1 / γ ) ) O(\log(1/γ)) O ( log ( 1/ γ )) dependence on the generalized margin. The paper improves competitive and dynamic regret bounds for smoothed online learning.
problem Smoothed online learning with hitting and switching costs.
method Optimization problems to minimize hitting cost, dynamic regret modification of existing algorithms.
result Improved competitive and dynamic regret bounds for various function classes.
Improved learning algorithms with privacy using smoothed analysis.
problem Designing robust and private learning algorithms.
method Smoothed analysis of adversarial and differentially private learning.
result Stronger regret and privacy error guarantees with smoothed adversaries.
Paper develops algorithms for PWA systems with polynomial regret.
problem Learning in piecewise affine systems due to discontinuities.
method Smoothed online learning framework applied to PWA systems.
result First algorithms with polynomial regret in PWA systems.
Paper improves probabilistic forecasts of electricity prices.
problem Combining multivariate probabilistic forecasts with dependencies.
method Online learning algorithm using Bernstein Online Aggregation (BOA).
result Significant improvement in CRPS over uniform combination.
We consider Online Convex Optimization (OCO) in the setting where the costs are m m m -strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive rat…
Optimizes sampling from target distributions with applications to online learning.
problem Optimizing the total variation distance between target and sampled distributions.
method Analyzes the sample complexity of approximate rejection sampling and its applications.
result The optimal total variation distance is given by $ ildeΘ( rac{D}{f'(n)})$ .
New algorithms reduce online learning regret by tracking gradient variation.
problem Online learning with unconstrained losses and gradient variation.
method Parameter-free algorithms with adaptive updates for L L L -smooth convex losses. result Regret bounds of order O ~ ( ∥ u ∥ V T ( u ) + L ∥ u ∥ 2 + G 4 ) \widetilde{O}(\|u\|\sqrt{V_T(u)} + L\|u\|^2+G^4) O ( ∥ u ∥ V T ( u ) + L ∥ u ∥ 2 + G 4 ) achieved without prior knowledge of comparator norm or Lipschitz constant. Unified analysis of online optimization with self-concordant barriers, improving regret bounds.
problem Online convex optimization with specific loss functions.
method Online mirror descent with self-concordant barriers and logarithmic loss.
result Improved regret bounds for online portfolio selection and quantum state learning.
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 complexity for smooth nonconvex optimization using quasi-Newton methods.
problem Finding ε-first-order stationary points of smooth functions with gradient information only.
method Two-level online learning approach involving quasi-Newton methods.
result Gradient complexity improved to O(d^(1/4)ε^(-13/8)) for d = O(ε^(-1/2)).
Here, we study different update rules in stochastic gradient descent (SGD) for online forecasting problems. The selection of the learning rate parameter is critical in SGD. However, it may not be feasible to tune this parameter in online learning. Therefore, it is necessary to have an update rule that is not sensitive …
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. Paper analyzes regret bounds for unconstrained online optimization.
problem Minimizing regret in dynamic online learning for strongly convex and smooth functions.
method Preconditioned OGD, Online Optimistic Newton (OON), multiple gradient queries.
result Achieves O ( C 2 , T ∗ ) O(C^*_{2,T}) O ( C 2 , T ∗ ) regret bound with one gradient query per round. New algorithm reduces regret in online learning for piecewise continuous functions.
problem Exponential loss in efficiency when moving from classical to adversarial learning.
method Introduces generalized bracketing numbers and Follow-the-Perturbed-Leader algorithm.
result Optimal scaling of optimization oracle calls with average regret.
Adaptive Bayesian learning aggregates experts to improve performance.
problem Bayesian online learning's performance depends on inferential choices.
method Treat Bayesian update rules as experts and aggregate them based on sequential predictive losses.
result The aggregate competes with the best expert in hindsight at a low aggregation cost.
SOOTT framework optimizes target tracking with robust and learning-augmented algorithms.
problem Optimizing target tracking in dynamic environments with adversarial perturbations.
method Integrates robust and learning-augmented algorithms for online decision-making.
result CoRT learning-augmented algorithm strictly improves over robust BEST when predictions are accurate.
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.
New algorithm reduces TV-denoising to adaptive online learning.
problem Estimating TV-bounded functions from noisy samples.
method Deep connection to Strongly Adaptive online learning; O ( n log n ) O(n \log n) O ( n log n ) time algorithm. result Near minimax optimal rate of O ( n 1 / 3 C n 2 / 3 ) O(n^{1/3}C_n^{2/3}) O ( n 1/3 C n 2/3 ) under squared error loss. This work explains why online imitation learning improves faster than theory predicts.
problem Online imitation learning's empirical policy improvement speed exceeds theoretical predictions.
method The authors analyze online imitation learning with a convex, smooth, and non-negative loss function, proving policy improvement in expectation and high probability.
result Adopting a sufficiently expressive policy class in online IL increases both policy improvement speed and performance bias.
New insights into learning from distributional adversaries and private data.
problem Understanding minimal assumptions for learning and generalization under distributional constraints.
method Generalized smoothness as a characterization of learnability and privacy under distributional adversaries.
result Near complete characterization of families that admit learnability and privacy under distributional adversaries.
New framework for understanding adversarial and stochastic learning.
problem Understanding the continuum from adversarial to stochastic settings in online learning.
method Distributionally constrained adversaries framework.
result Characterization of learnable distribution classes for various function classes.
Smooth calibration improves forecast reliability even with leaked information.
problem Improving forecast reliability with leaked information.
method Combining nearby forecasts to ensure smooth calibration, which can be guaranteed by deterministic procedures.
result Smooth calibration can be guaranteed by deterministic procedures even with leaked forecasts, and it yields uncoupled finite-memory dynamics in games.
New algorithm reduces online learning iterations by a factor of T^2/3.
problem Efficiency in online learning with smooth cost functions.
method Follow-the-Perturbed-Leader method using online primal-dual framework.
result Guaranteed T^2/3 regret for general online convex optimization.
Improved online convex optimization bounds between stochastic and adversarial settings.
problem Understanding optimization tasks that are neither i.i.d. nor fully adversarial.
method Establishing novel regret bounds exploiting smoothness of expected losses.
result Regret bounds improve on previous results by reducing dependence on maximum gradient length to variance of gradients.
Study bandit problem on smooth graph functions for recommender systems.
problem Online learning problems involving graphs, like content-based recommendation.
method Introduced spectral bandit problem and two algorithms that scale linearly in effective dimension.
result Learned user preferences for thousands of items from just tens nodes evaluations.
We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us to derive the no-regret properties of a large class of discrete-time algorithms i…
A novel online framework for analyzing multidimensional functional data.
problem Analysis of multidimensional functional data streams poses significant challenges.
method Online functional principal component analysis using tensor product splines on a Stiefel manifold with Riemannian stochastic gradient descent.
result Efficient and scalable modeling of multidimensional functional data.
We study online optimization of smoothed piecewise constant functions over the domain [0, 1). This is motivated by the problem of adaptively picking parameters of learning algorithms as in the recently introduced framework by Gupta and Roughgarden (2016). Majority of the machine learning literature has focused on Lipsc…
Improved regret bounds for online convex optimization under stochastic and adversarial settings.
problem Interpolating between stochastic and adversarial online convex optimization.
method Optimistic online mirror descent (OMD) for the Stochastically Extended Adversarial (SEA) model.
result Established new regret bounds for various function classes.
Study optimizes online learning for vector-valued data regression.
problem Approximating regression functions from noisy vector-valued data.
method Online learning algorithm using RKHS, with error analysis.
result Order-optimal estimate of expected squared error.
New analysis shows how temporal variability affects online learning performance.
problem Understanding the impact of temporal variability on online learning performance.
method Careful regret analysis and adaptive algorithm development.
result Proved a novel static regret bound that depends on temporal variability.
Optimal online learning for joint pricing and resource allocation.
problem Maximizing net profit in dynamic pricing and resource allocation with stochastic demand.
method Developed an efficient algorithm using a Lower-Confidence Bound (LCB) meta-strategy over multiple OCO agents.
result Achieved i l d e O ( T m n ) ilde{O}(\sqrt{Tmn}) i l d e O ( T mn ) regret, optimal with respect to time horizon T T T . We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain "sufficient statistics" for the data sequence, then there exists a special Burkholder function that 1) can be used algorithmically to achieve the regret bound and 2) only depends on these suffic…
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…
The paper tackles a bandit problem on graphs with smooth functions, aiming to recommend items with high expected ratings.
problem Online learning problems involving graphs, such as content-based recommendation.
method Introduced the notion of effective dimension and proposed two algorithms for solving the problem.
result The algorithms can learn good estimators of user preferences from just tens of nodes evaluations.
Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
problem Adversarial online nonparametric regression with general convex losses.
method Parameter-free learning algorithm leveraging chaining trees to compete against H{ö}lder functions, dynamically tracking and adapting to local smoothness variations.
result First computationally efficient algorithm with locally adaptive optimal rates for online regression in an adversarial setting.