New method reduces variance in complex probabilistic model optimization.
problem High variance in stochastic optimisation of complex models.
method Use recognition network to approximate optimal control variate for each mini-batch.
result Sub-optimal variance reduction is improved with new approach.
PALS extends PAL for optimizing stochastic simulators efficiently.
problem Optimizing stochastic simulators with high output variance and expensive evaluations.
method Bayesian optimization with probabilistic models, extending PAL for stochastic settings.
result PALS outperforms other methods in optimizing stochastic simulators.
Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate models for stochastic minimization and learning problems that exhibit better robu…
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic continuous optimization, namely stochastic gradient descent and its variants, to such d…
We show that dropout training is best understood as performing MAP estimation concurrently for a family of conditional models whose objectives are themselves lower bounded by the original dropout objective. This discovery allows us to pick any model from this family after training, which leads to a substantial improvem…
HA-SME models SGD dynamics with Hessian info for better escaping behaviors.
problem Capturing the escaping behaviors of SGD from stationary points.
method HA-SME, a novel SDE with Hessian info in drift and diffusion.
result HA-SME achieves best approximation error and recovers SGD dynamics for quadratics.
We study convergence properties of Stochastic Gradient Descent (SGD) for convex objectives without assumptions on smoothness or strict convexity. We consider the question of establishing that with high probability the objective evaluated at the candidate minimizer returned by SGD is close to the minimal value of the ob…
The objective optimization of medical imaging systems requires full characterization of all sources of randomness in the measured data, which includes the variability within the ensemble of objects to-be-imaged. This can be accomplished by establishing a stochastic object model (SOM) that describes the variability in t…
Conditional stochastic optimization covers a variety of applications ranging from invariant learning and causal inference to meta-learning. However, constructing unbiased gradient estimators for such problems is challenging due to the composition structure. As an alternative, we propose a biased stochastic gradient des…
Proposes new stochastic algorithms for multi-objective optimization.
problem Multi-objective optimization in machine learning problems.
method Direction-oriented multi-objective formulation and Stochastic Direction-oriented Multi-objective Gradient descent (SDMGrad).
result Stochastic algorithms converge to Pareto stationary points with improved complexities.
Derivative-free method solves stochastic optimization problems with noisy objectives and constraints.
problem Solving nonlinear optimization problems with stochastic objectives and deterministic constraints using only zero-order information.
method Derivative-Free Stochastic Sequential Quadratic Programming (DF-SSQP) method using simultaneous perturbation stochastic approximation (SPSA) for gradient and Hessian estimation.
result Global almost-sure convergence of the DF-SSQP method under standard assumptions, with local asymptotic normality and statistical inference.
A new algorithm reduces communication rounds for distributed convex optimization.
problem Efficiently solving convex optimization problems in distributed systems.
method Proposes a stochastic Newton algorithm for homogeneous distributed stochastic convex optimization.
result Reduces the number and frequency of communication rounds compared to existing methods.
Study on Pareto optimality in multi-objective bandit problems.
problem Pareto optimality in multi-objective multi-armed bandit problems.
method Formulated adversarial multi-objective multi-armed bandit, defined Pareto regrets, presented algorithms, established upper and lower bounds.
result New algorithms are optimal in adversarial settings and nearly optimal in stochastic settings.
Generative model learns object variability from MRI measurements.
problem Establishing stochastic object models from medical imaging data.
method Advanced AmbientGANs with multiresolution training.
result AmbientGANs reliably learn object distributions from incomplete or noisy data.
Develops a new method to improve performance in multi-objective learning problems.
problem Gradient bias in multi-objective learning leading to degraded performance.
method Stochastic Multi-objective gradient Correction (MoCo) method that guarantees convergence without increasing batch size.
result Demonstrates effectiveness of MoCo method in simulations on multi-task learning.
Real-world dynamical systems often consist of multiple stochastic subsystems that interact with each other. Modeling and forecasting the behavior of such dynamics are generally not easy, due to the inherent hardness in understanding the complicated interactions and evolutions of their constituents. This paper introduce…
New method solves optimization problems with stochastic objectives and constraints.
problem Optimization problems with stochastic objectives and deterministic constraints.
method Trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method.
result Global almost-sure convergence to first-order stationary points under standard assumptions.
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial intelligence and machine learning, such as fused Lasso, fused logistic regression, a…
Develops a new method to create object models from medical images.
problem Variability in anatomical structures and textures limits observer performance.
method Progressive Growing AmbientGAN (ProAmGAN) for creating stochastic object models from medical imaging measurements.
result Demonstrates the effectiveness of ProAmGAN in creating realistic object models.
New method solves stochastic optimization problems with random models.
problem Optimizing stochastic objectives with deterministic constraints.
method Trust-Region Sequential Quadratic Programming with random model.
result Global convergence guarantees for first- and second-order stationary points.
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.
We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions. In particular, the results are applicable to simple objective functions arising in machine learning.
We empirically evaluate a stochastic annealing strategy for Bayesian posterior optimization with variational inference. Variational inference is a deterministic approach to approximate posterior inference in Bayesian models in which a typically non-convex objective function is locally optimized over the parameters of t…
Bayesian optimization on networks using Gaussian process models.
problem Optimizing expensive black-box functions on network structures.
method Developed Bayesian optimization algorithms with Gaussian process surrogates tailored to network geometry.
result Established regret bounds for smooth objective functions and analyzed practical cases.
The paper solves stochastic control problems with implicit objectives, finding equilibrium strategies.
problem Stochastic control problems with implicitly defined objectives leading to time-inconsistency.
method Closed-loop equilibrium solutions in a controlled diffusion framework, providing sufficient and necessary conditions.
result Explicit characterization of equilibrium portfolio strategies in terms of ordinary differential equations.
Study shows convergence of stochastic gradient method for unregularized Wasserstein optimization.
problem Wasserstein distributionally robust optimization under potential distribution shifts.
method Regularized approximation with stochastic gradient methods, convergence analysis.
result Stochastic gradient method converges to subgradients of unregularized objective as regularization vanishes.
New method learns stochastic process representations without exact reconstruction.
problem Learning exact representations of high-dimensional noisy stochastic processes.
method CReSP framework for contrastive learning of stochastic processes.
result Effective for learning representations of various stochastic processes.
Develops minibatch stochastic proximal gradient for large-scale learning models.
problem Finding optimal predictors with complex regularizers in large-scale learning models.
method Minibatch variants of stochastic proximal gradient algorithm for composite objective functions.
result Minibatch size N after O(Nε1) iterations achieves ε−suboptimality in expected quadratic distance. Develops a new method for efficient stochastic bilevel optimization.
problem Stochastic bilevel optimization problems in machine learning applications.
method Single-Timescale stochAstic BiLevEl optimization (STABLE) method.
result Achieves the same order of sample complexity as stochastic gradient descent for single-level optimization.
Paper proposes a second-order method for faster SVI convergence.
problem Poor convergence rate of first-order SVI algorithms.
method Derives Hessian matrix and implements two numerical schemes for efficient second-order SVI.
result Proposed approach achieves faster convergence compared to first-order SVI.
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)-stationary points. Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. The parameter …
New method ranks multivariate distributions in SMOOP using q-dominance.
problem Lack of reliable methods to rank multivariate distributions in SMOOP.
method Introduces center-outward q-dominance and develops empirical test procedures.
result Proves q-dominance implies FSD and establishes a sample size threshold.
New algorithm solves stochastic optimization problems with unknown gradients.
problem Solving nonlinear optimization problems with stochastic objectives and deterministic constraints.
method Adaptive SQP with differentiable exact augmented Lagrangian and stochastic line search.
result Global convergence established for both non-adaptive and adaptive SQP methods.
YOASOVI improves stochastic VI for large models with fast, self-correcting sampling.
problem Efficiently performing stochastic Variational Inference on large Bayesian models.
method YOASOVI uses acceptance sampling to draw only one sample per iteration, improving convergence speed and accuracy.
result YOASOVI converges faster and more accurately than regular Monte Carlo and Quasi-Monte Carlo methods.
Combines Gaussian processes and polynomial chaos for stochastic control.
problem Uncertainties in dynamic models lead to performance issues in predictive control.
method Combines Gaussian processes with polynomial chaos expansions to estimate probability distributions of nonlinear functions.
result Demonstrates accurate approximation and closed-loop performance in stochastic nonlinear model predictive control.
New framework improves stochastic optimization for variational inference.
problem Improving variational posterior approximations in high-dimensional models.
method Developed a robust stochastic optimization framework using Markov chains.
result Demonstrated improved accuracy and robustness across diverse models.
This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale behaviors, then in a large learning rate regime which only resolves the macroscopic but n…
SUSTAIN algorithm tackles stochastic bilevel optimization with near-optimal complexity.
problem Stochastic bilevel optimization problems with specific convexity and smoothness properties.
method SUSTAIN algorithm using single-timescale double-momentum stochastic approximation.
result SUSTAIN achieves near-optimal complexity for finding ε-stationary solutions.
Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic type. We study the stochastic multi-gradient (SMG) method, seen as an extension of…
Bayesian method reduces misclassification errors in ranking Pareto-optimal solutions.
problem Identifying true Pareto-optimal solutions in noisy multiobjective optimization.
method Sequential allocation of extra samples using stochastic kriging to build predictive distributions.
result The proposed method outperforms existing algorithms in reducing misclassification errors.
GENESIS-V2 infers unordered object representations without iterative refinement.
problem Unsupervised learning of unordered object representations for complex images.
method Stochastic stick-breaking process for clustering pixel embeddings.
result GENESIS-V2 outperforms recent baselines in unsupervised image segmentation and scene generation.
Study improves sampling efficiency of diffusion models using RL and PDEs.
problem Training neural stochastic differential equations without access to target samples.
method Proves equivalences between RL methods and PDEs, uses coarse time discretization.
result Improves sample efficiency and reduces computational cost.
RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments c…
Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assu…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and the objective function. Since the problem has unbounded domain, the objective func…
New technique reduces bias in CSO problems, improving sample complexity.
problem Reducing bias in conditional stochastic optimization problems.
method Introducing a stochastic extrapolation technique combined with variance reduction.
result Achieved significantly better sample complexity for nonconvex smooth objectives.
This work analyzes SGD for SGMs, providing convergence rates and error bounds.
problem Optimization dynamics of SGMs trained with stochastic gradients.
method Non-convex convergence rate analysis and Neural Tangent Kernel analysis.
result Theoretical insights into SGD convergence and error bounds for SGMs.