New algorithm reduces optimization complexity in adaptive mirror descent.
problem Optimizing complex, non-smooth, non-convex functions efficiently.
method SVRAMD: Variance Reduced Adaptive Mirror Descent.
result Variance reduction accelerates convergence in adaptive mirror descent.
New algorithms reduce regret in both stochastic and deterministic environments.
problem Designing algorithms that perform well in both types of MDPs.
method Proposed new environment norms and algorithms with variance-dependent regret bounds.
result First algorithm with simultaneously optimal bounds for both stochastic and deterministic MDPs.
Memory-efficient algorithm reduces variance in off-policy RL.
problem High variance in off-policy policy optimization.
method Memory-efficient, stochastically variance-reduced algorithm using off-policy samples.
result Empirically validated effectiveness of the proposed algorithm.
Develops Thompson Sampling algorithms for mean-variance bandits.
problem Risk in online decision making systems.
method Thompson Sampling algorithms for mean-variance MAB with comprehensive regret analyses.
result Achieves best known regret bounds for mean-variance MABs and information-theoretic bounds in some regimes.
New algorithms improve best-arm identification with varying rewards.
problem Identifying the best arm with varying reward variances in fixed budget.
method Proposed two algorithms: SHVar for known variances, SHAdaVar for unknown variances; uses non-uniform budget allocation.
result Bounding misidentification probabilities for both algorithms.
Increasing variance of losses improves learning with noisy labels.
problem Learning with noisy labels and the need to penalize variance of losses.
method Designing regularizers based on the label noise transition matrix to increase variance of losses.
result Increasing variance of losses significantly improves generalization ability.
New algorithm optimizes multi-armed bandit performance in stochastic and adversarial settings.
problem Optimizing multi-armed bandit performance in both stochastic and adversarial environments.
method Follow-the-regularized-leader method with adaptive learning rates.
result First BOBW algorithm with gap-variance-dependent regret bounds in adversarial settings.
New dropout technique reduces variance and overestimation in deep Q-Learning.
problem Reduction of variance and overestimation in deep Q-Learning.
method Using Dropout techniques to reduce variance and overestimation in deep Q-Learning.
result Demonstrated effectiveness in enhancing stability and reducing both variance and overestimation.
The paper develops a robust algorithm for contextual bandits with heavy-tailed rewards.
problem Contextual bandits with heavy-tailed rewards.
method Develops an algorithm based on Catoni's estimator for robust statistics, applying it to contextual bandits with general function approximation.
result Establishes regret bounds that depend on cumulative reward variance and logarithmically on the reward range and number of rounds.
Develops a new SPP algorithm with variance reduction for weakly convex optimization.
problem Weakly convex, composite optimization problems.
method Inexact semismooth Newton framework with variance reduction for stochastic proximal point updates.
result Establishes convergence results for the proposed algorithm.
Paper introduces control variate to reduce variance in off-policy reinforcement learning.
problem High variance in off-policy reinforcement learning.
method Introduces control variate technique to Expected Sarsa(λ) and proposes ES(λ)-CV algorithm.
result Proposed ES(λ)-CV algorithm has lower variance than Expected Sarsa(λ).
New algorithm reduces regret for linear bandits with unknown noise variance.
problem Finding optimal actions in linear bandits with varying noise variance.
method Adaptive algorithm with Freedman-type concentration inequality and multi-layer structure.
result Achieves i l d e O ( d ∑ k = 1 K σ k 2 + d ) ilde{O}(d \sqrt{\sum_{k = 1}^K σ_k^2} + d) i l d e O ( d ∑ k = 1 K σ k 2 + d ) regret for linear bandits. New algorithm improves convergence of AUC maximization.
problem Optimizing AUC for imbalanced classes with stochastic methods.
method Variance Reduced Stochastic Proximal Algorithm for AUC Maximization (VRSPAM).
result VRSPAM converges faster than previous methods.
Managing risk in dynamic decision problems is of cardinal importance in many fields such as finance and process control. The most common approach to defining risk is through various variance related criteria such as the Sharpe Ratio or the standard deviation adjusted reward. It is known that optimizing many of the vari…
Neural- σ 2 σ^2 σ 2 -LinearUCB improves regret in neural contextual bandits.
problem Balancing exploration and exploitation in neural contextual bandits.
method Proposes a variance-aware neural UCB algorithm using neural representations and an upper bound of reward noise variance.
result Oracle and practical versions of Neural- σ 2 σ^2 σ 2 -LinearUCB achieve better regret guarantees and performance. Paper improves sparse linear bandits by accounting for noise variance.
problem Sparse linear bandits with unknown noise variance.
method Develops a general framework to convert variance-aware algorithms to sparse linear bandits.
result Achieves $\widetilde{\mathcal O}\left(\sqrt{d\sum_{t=1}^T σ_t^2} + 1
ight)$ regret, interpolating between worst-case and benign settings.
A new algorithm SRG-DQN reduces variance in deep Q-learning.
problem Inaccurate estimation of anchor points in SVRG for deep Q-learning.
method Introduces recursive gradient variance reduction for stochastic gradient updates.
result Demonstrates improved efficiency and effectiveness of SRG-DQN on reinforcement learning tasks.
New algorithm for training GNNs with learned weights.
problem Optimal sampling for GNNs with learned weights is intractable.
method Formulated as an adversary bandit problem, optimizing exploration and exploitation.
result Asymptotically approaches optimal variance within a factor of 3.
Algorithm estimates common mean from Gaussian variables with unknown variances.
problem Estimating common mean from Gaussian variables with different unknown variances.
method Intuitive and efficient algorithm using Subset-of-Signals model as benchmark.
result Improved estimation error by polynomial factors compared to previous work.
The paper explores trade-offs between regret and variance in online learning algorithms.
problem Investigating the trade-offs between regret and variance in online learning.
method Analysis of the Exponentially Weighted Average (EWA) algorithm and its variants.
result A variant of EWA either achieves negative regret or guarantees a logarithmic bound on both variance and regret.
Paper develops momentum schemes with variance reduction for non-convex composition optimization.
problem Lack of convergence guarantee and efficient momentum design in existing algorithms.
method Develops various momentum schemes with SPIDER-based variance reduction.
result Achieves near-optimal sample complexity and linear convergence rate.
We present an actor-critic framework for MDPs where the objective is the variance-adjusted expected return. Our critic uses linear function approximation, and we extend the concept of compatible features to the variance-adjusted setting. We present an episodic actor-critic algorithm and show that it converges almost su…
Unified framework for variance reduction to solve monotone operator problems.
problem Large-scale monotone inclusion problems with finite sum structure.
method Developed a general framework for variance-reduced forward-backward splitting algorithms.
result Linear convergence rate under mild assumptions, with Catalyst acceleration and asynchronous implementation.
Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizer. The existing convergence results assume uniform data sampling with replacement. However, it has been observed in …
VRER selectively reuses past observations to reduce variance in policy optimization.
problem Lack of effective experience replay for accelerating policy optimization in complex systems.
method Variance Reduction Experience Replay (VRER) framework that selectively reuses informative samples.
result VRER reduces gradient variance and improves policy learning over state-of-the-art algorithms.
Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms are usually slow to converge and achieve sub-linear convergence rates, due to t…
Estimates algorithmic variance for bagging and random forests using bootstrap.
problem Deciding when an ensemble is large enough for accurate predictions.
method Bootstrap method to estimate algorithmic variance under a first-order model.
result Consistent approximation of the centered law of prediction error as ensemble size increases.
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.
VRCQ algorithm reduces variance in Q-learning for MDPs, achieving optimal sample complexity.
problem Estimating the optimal Q-function in MDPs with synchronous sampling.
method VRCQ combines direct variance reduction and Cascade Q-learning.
result VRCQ is minimax optimal and instance optimal for single-action problems.
A novel k-NN method estimates conditional mean and variance efficiently.
problem Joint estimation of conditional mean and variance.
method Integrates k-NN with automated variance selection.
result Achieves fast convergence rates and improved precision.
We study optimization algorithms based on variance reduction for stochastic gradient descent (SGD). Remarkable recent progress has been made in this direction through development of algorithms like SAG, SVRG, SAGA. These algorithms have been shown to outperform SGD, both theoretically and empirically. However, asynchro…
Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.
problem Minimizing regret in Gaussian process bandits with unknown reward functions.
method New upper bound on maximum posterior variance, refined MVR and PE algorithms.
result Optimal regret bounds for noiseless, varying noise, and RKHS norms.
Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high vari…
New algorithms reduce variance in solving complex mathematical problems.
problem Solving convex-concave saddle point problems, variational inequalities, and inclusions.
method Stochastic variance reduction for extragradient, forward-backward-forward, and forward-reflected-backward methods.
result All proposed methods converge with complexities matching or improving deterministic counterparts.
MARS optimizes large model training by reducing variance, outperforming AdamW.
problem Training large models efficiently and scalably.
method Unified optimization framework MARS combining preconditioned gradient updates and variance reduction.
result MARS outperforms AdamW in training GPT-2 models.
The paper analyzes SW-SGD for MSE in biased and variance-reduced gradient estimators.
problem Analyzing MSE of SW-SGD in biased and variance-reduced gradient estimators.
method Using asymptotic normality, the paper characterizes SW-SGD's mean and variance, proving convergence and showing SW-SGD's superiority over SGD.
result SW-SGD incurs lower MSE than SGD on quadratic and convex problems.
We study finite-sum nonconvex optimization problems, where the objective function is an average of n n n nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with conventional stochastic variance reduced gradient (SVRG) algorithm that uses two reference …
UCB-V algorithm improves on UCB for MAB problems with variance estimates.
problem Optimizing arm selection in MAB problems with variance information.
method Asymptotic and high probability analysis of UCB-V algorithm.
result UCB-V can exhibit instability in arm-pulling rates but achieves refined regret bounds.
A new method reduces data valuation variance for more trustworthy data trading.
problem Data valuation and trustworthy data trading in algorithmic prediction.
method Variance reduced Shapley value estimation using stratified sampling.
result VRDS method reduces estimation variance and improves data marketplace development.
New scheme adapts batch size for faster variance-reduced algorithms.
problem Slowness of variance-reduced algorithms due to large batch size.
method Eliminates backtracking line search, adapts batch size via history stochastic gradients.
result Significantly reduces overall complexity for SVRG and SARAH/SPIDER.
Paper proposes diagnostics for error and variance estimation in randomized matrix computations.
problem Safe use of randomized matrix algorithms in applications.
method Leave-one-out error estimator and jackknife resampling method.
result Provides rapid diagnostics to assess quality of randomized matrix computations.
Improves Monte-Carlo simulations for consistent mean and variance.
problem Artificial randomness in running mean calculations.
method Combining running mean and variance with accurate summing.
result Increased accuracy and robustness of Monte-Carlo estimates.
Estimates Markov chain variance efficiently without storing samples.
problem Estimating the asymptotic variance of Markov chain functions.
method Linear stochastic approximation of Poisson equation solution.
result Optimal MSE convergence rate with finite sample guarantees.
SVRN accelerates Newton methods by reducing variance and improving performance.
problem Improving the efficiency of Newton methods for large-scale optimization problems.
method Stochastic Variance-Reduced Newton (SVRN) algorithm that accelerates Subsampled Newton and Iterative Hessian Sketch algorithms.
result SVRN accelerates Newton methods by reducing the number of passes over the data, achieving a significant improvement in performance.
New sparsity operator reduces variance reduction methods' computational cost.
problem Reduce computational cost of variance reduction methods.
method Introduce random-top-k operator to estimate gradient sparsity and reduce operations per update.
result Our algorithm consistently outperforms SpiderBoost in various tasks.
Stochastic gradient descent updates parameters with summation gradient computed from a random data batch. This summation will lead to unbalanced training process if the data we obtained is unbalanced. To address this issue, this paper takes the error variance and error mean both into consideration. The adaptively adjus…
New algorithm offers costless model selection in contextual bandits.
problem Minimizing cumulative regret in stochastic contextual bandits.
method Gradually increasing class complexity and adapting to the simplest class with dominant estimation variance.
result Costless model selection is feasible under certain conditions, providing improved regret guarantees.
Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare. The mean-variance function is one of the most widely used objective functions in risk management due to its simplicity and interpretability. Existing algorithms for mean-…