Efficiently optimizes expensive functions with multi-step lookahead using one-shot optimization.
problem Optimizing expensive functions with long-term impacts using myopic approaches.
method Formulated as nested optimization problems within a multi-step scenario tree, optimized in one-shot fashion.
result Multi-step expected improvement is computationally tractable and outperforms existing methods.
New algorithm improves stability of optimization algorithms by adapting step-size.
problem Optimization algorithms' effectiveness is sensitive to step-size hyperparameters.
method Adapts NGN step-size method with momentum to enhance stability.
result Achieves convergence rate of O(1/√K) without restrictive assumptions.
Step decay schedules improve convergence in non-convex optimization.
problem Improving convergence in non-convex optimization problems.
method Analyzing convergence rates of step decay schedules in non-convex, convex, and strongly convex problems.
result Step decay schedules achieve O ( ln T / T ) \mathcal{O}(\ln T/\sqrt{T}) O ( ln T / T ) convergence rates in various optimization scenarios. Proposes a neural network for learning step-size policies for L-BFGS optimization.
problem Optimizing step sizes for L-BFGS in large-scale problems.
method Neural network architecture using local iterate information, trained via stochastic optimization.
result Outperforms existing step size selection methods in training classifiers.
We propose a population-based Evolutionary Stochastic Gradient Descent (ESGD) framework for optimizing deep neural networks. ESGD combines SGD and gradient-free evolutionary algorithms as complementary algorithms in one framework in which the optimization alternates between the SGD step and evolution step to improve th…
Multiple gossip steps improve decentralized optimization convergence.
problem Efficiently optimizing large-scale machine learning models with limited communication.
method Integrates multiple gossip steps between gradient descent iterations in compressed decentralized optimization.
result Convergence to within ε of the optimal value for smooth non-convex objectives.
Adaptive step-size improves optimization in complex geometries.
problem Optimizing functions with non-Euclidean geometries.
method Adaptive step-size strategy for optimization algorithms.
result Guaranteed convergence for Adaptive Conditional Gradient Descent.
New adaptive step-size method for convex optimization without tuning.
problem Optimizing convex functions efficiently with stochastic gradients.
method Adapted Adaptive Gradient Descent Without Descent to stochastic setting.
result Stochastic gradient descent converges under various assumptions.
A new method approximates expected empirical loss for stochastic deep learning tasks.
problem Determining optimal step sizes for stochastic gradient descent in deep learning.
method Applying one-dimensional function fitting to noisy losses of vertical cross sections to approximate expected empirical loss.
result The method leads to a robust and straightforward optimization method that performs well across datasets and architectures.
Random Function Descent improves optimization in high dimensions.
problem Lack of effective optimization methods in high-dimensional spaces.
method Introducing a 'random function' framework to optimize classical optimization problems.
result Random Function Descent (RFD) is a scalable optimization method that bridges Bayesian and classical optimization.
A major challenge in current optimization research for deep learning is to automatically find optimal step sizes for each update step. The optimal step size is closely related to the shape of the loss in the update step direction. However, this shape has not yet been examined in detail. This work shows empirically that…
Optimizes random forest inference by defining step order to maximize accuracy.
problem Limited inference time in resource-constrained systems.
method Designs anytime random forest algorithm on step granularity, proposing optimal step order.
result Backward Squirrel Order performs nearly as well as the optimal step order.
Optimal transport method rejects new classes and adjusts class ratios for open set domain adaptation.
problem Handling new classes in target domains with distribution shifts.
method Two-step optimal transport approach: reject new classes first, then adjust class ratios.
result Outperforms state-of-the-art methods in open set domain adaptation.
In smooth strongly convex optimization, knowledge of the strong convexity parameter is critical for obtaining simple methods with accelerated rates. In this work, we study a class of methods, based on Polyak steps, where this knowledge is substituted by that of the optimal value, f ∗ f_* f ∗ . We first show slightly improved …
Efficient deep policy gradient method for continuous-time control problems.
problem Optimal control in continuous time with fine time discretization.
method Multi-scale deep policy gradient method with varying time discretization.
result Targeted efficiency in computational resources achieved through multi-scale approach.
Paper uses RL to optimize daily step distribution for better health biomarkers.
problem Lack of personalized PA distribution recommendations for health biomarkers.
method Developed an offline reinforcement learning algorithm to learn optimal PA distributions.
result Learned optimal policy suggests more consistent daily steps and tailored recommendations.
Develops a generalized version of Chung's Lemma for stochastic optimization methods.
problem Establishing asymptotic convergence rates for stochastic optimization methods under various step size rules.
method Generalized version of Chung's Lemma for a broader family of step size rules.
result Demonstrates tight non-asymptotic convergence rates for various stochastic methods.
New SPS variant improves non-smooth optimization without small gradients.
problem Improving non-smooth optimization without small gradients.
method Safeguarded Stochastic Polyak Step Size (SPS s a f e _{safe} s a f e ) for non-smooth optimization. result Rigorous convergence guarantees for non-smooth convex optimization without strong assumptions.
New algorithm learns optimal policy with multi-step lookahead information.
problem Learning optimal policy in reinforcement learning with multi-step lookahead information is NP-hard.
method Adaptive batching policies that process lookahead in state-dependent chunks.
result Order-optimal regret bounds up to a constant factor of lookahead horizon.
Stochastic algorithm achieves sublinear convergence for bi-objective optimization.
problem Optimizing two conflicting functions using gradient or subgradient descent.
method Stochastic alternating algorithm with varying steps for each objective.
result Achieves sublinear convergence rate of O(1/T) under strong convexity.
Postprocessing reduces Bayesian optimization steps for global optima.
problem Slow convergence in Bayesian optimization for high-dimensional problems.
method Prohibits duplicated samples in the dataset postprocessing method.
result Significantly reduces the number of sequential steps to find the global optimum.
Study optimizes step size for Metropolis algorithm in non-identifiable cases.
problem Optimizing step size for Metropolis algorithm in non-identifiable models.
method Analytical derivation of average acceptance rate for non-identifiable cases.
result Developed optimization principle for step size based on average acceptance rate.
Proposes a new algorithm for solving optimization problems with stochastic objectives and equality constraints.
problem Optimization problems with stochastic objectives and deterministic equality constraints.
method Trust-region stochastic sequential quadratic programming (TR-StoSQP) with adaptive relaxation techniques.
result Established a global almost sure convergence guarantee for TR-StoSQP.
Global optimization in Bayesian inference yields little additional benefit.
problem Improving psychometric parameter estimation using global optimization strategies.
method Experimental simulations comparing myopic and global strategies in multiple models.
result Global optimization strategies provide negligible additional utility improvement beyond the immediate next steps.
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
problem Optimizing Bayesian filtering with deterministic particles to avoid degeneration.
method Progressive flow of particles through a sequence of sub-steps, each using an optimal transport map to replace non-equally weighted particles with equally weighted ones.
result The method avoids particle degeneration and simplifies the filtering process by not requiring inversions or monotonicity constraints.
Researchers describe Casimir functions for 3- and 4-step nilpotent Lie groups.
problem Understanding Casimir functions for free nilpotent Lie groups of steps 3 and 4.
method Construction of Casimir functions for free nilpotent Lie groups of steps 3 and 4.
result For 3-step groups, coadjoint orbits are fully described as affine subspaces or direct products of quadrics.
A new method learns straight trajectories in one step for optimal flow matching.
problem Learning flows with straight trajectories for fast inference.
method Optimal Flow Matching (OFM) approach using convex functions for vector fields.
result Recovering straight OT displacements in just one FM step for quadratic transport.
New SAGA algorithm with decreasing step for stochastic optimization.
problem Analysis of SAGA algorithm and its convergence properties.
method Introducing a new λ-SAGA algorithm with decreasing step, investigating convergence and establishing a central limit theorem.
result Established convergence and central limit theorem for λ-SAGA algorithm.
QAOA matches classical tensor power iteration in spiked tensor model recovery.
problem Statistical estimation in spiked tensor model with computational gap.
method Analysis of QAOA performance on spiked tensor model.
result QAOA weak recovery threshold matches tensor power iteration.
A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DI…
We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In contrast to traditional phenomenological works that aim to learn a generative model to fit the behavioral data, we propose a novel variational principle and treat user …
New gradient methods solve multiscale optimization problems efficiently.
problem Minimizing functions with multiple non-interacting smooth, strongly convex components.
method Big-Step-Little-Step interleaving of standard methods.
result Complexity bound scales as product of square-roots of condition numbers of components, improving on accelerated gradient methods.
Optimal private ERM and SCO with subquadratic gradient complexity.
problem Private optimization of non-smooth convex functions.
method Subquadratic gradient complexity algorithm using subsampling and smoothing.
result Achieved optimal excess empirical risk and population loss.
We present SEBOOST, a technique for boosting the performance of existing stochastic optimization methods. SEBOOST applies a secondary optimization process in the subspace spanned by the last steps and descent directions. The method was inspired by the SESOP optimization method for large-scale problems, and has been ada…
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used. Our algorithm consists of two steps; one is the direction estimate step and the o…
New algorithm for sampling from distributions with thin tails.
problem Sampling from distributions with thin tails and theoretical guarantees.
method Proposes a Metropolized Algorithm With Optimization Step (MAO).
result Derives upper bounds on the mixing time of MAO.
Avare improves optimization and sampling with adaptive importance sampling.
problem Improving convergence rate of stochastic gradient-based algorithms.
method Adaptive importance sampling with decreasing step-sizes.
result Achieves dynamic regret bounds of O ( T 2 / 3 ) \mathcal{O}(T^{2/3}) O ( T 2/3 ) and O ( T 5 / 6 ) \mathcal{O}(T^{5/6}) O ( T 5/6 ) . Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.
TREGO improves EGO for global optimization of high-dimensional problems.
problem Efficient Global Optimization struggles with high dimensions and lacks theoretical guarantees.
method TREGO alternates between EGO steps and local steps within a trust region.
result TREGO outperforms EGO and other methods in black-box optimization problems.
New k k k -step policy gradient method avoids local optima in restricted policy classes.
problem Suboptimal local optima in policy gradient methods for restricted policy classes.
method Proposes a k k k -step policy gradient method to escape myopic local optima. result The method converges to near optimal solutions exponentially close to the optimal deterministic policy.
Although ADAM is a very popular algorithm for optimizing the weights of neural networks, it has been recently shown that it can diverge even in simple convex optimization examples. Several variants of ADAM have been proposed to circumvent this convergence issue. In this work, we study the ADAM algorithm for smooth nonc…
Chebyshev steps improve convergence in deep-unfolded gradient descent.
problem Improving convergence speed in iterative algorithms.
method Introducing Chebyshev steps to bound convergence rate of gradient descent.
result Chebyshev steps lead to asymptotically optimal convergence rate.
Optimistic method adapted for faster convex-concave min-max problems.
problem Solving convex-concave min-max optimization problems efficiently.
method Adaptive, line search-free second-order methods combining optimistic updates and second-order information.
result Achieves optimal convergence rate without line search or backtracking.
Guarantees for tuning step size using meta-gradient descent.
problem Choosing optimal parameters for optimization algorithms.
method Learning-to-learn approach with meta-gradient descent.
result Meta-gradient can explode/vanish, requiring careful meta-objective design.
Efficiently optimizes constrained problems with two-step lookahead BO.
problem Optimizing constrained problems with limited computational resources.
method Two-step lookahead Bayesian optimization with inequality constraints, using a novel unbiased gradient estimator.
result Significantly improves query efficiency over previous methods.
Paper introduces a privacy-preserving line search method for optimization.
problem Optimization performance depends on step size tuning, which is difficult and privacy-sensitive.
method Introduces a stochastic adaptive line search algorithm that satisfies differential privacy.
result The algorithm efficiently uses privacy budget and outperforms existing private optimizers.
A new method automatically and dynamically sets learning rates in deep learning.
problem Determining the appropriate learning rate in deep learning tasks is challenging and often subjective.
method Local Quadratic Approximation (LQA) to automatically and dynamically set learning rates.
result The proposed method leads to nearly optimal learning rates in a computationally efficient way.
VMBPO optimizes model and policy jointly using variational lower-bound.
problem Data efficiency in RL with biased simulated data.
method Formulate variational objective function, use EM, iteratively improve model and policy.
result VMBPO is more sample-efficient and robust than model-free algorithms.