Method solves complex optimization problems with high probability bounds.
problem Nonlinear equality constrained stochastic optimization problems.
method Step-search sequential quadratic programming method.
result High-probability bound on iteration complexity for first-order stationarity.
Study optimal hedging for claims with random weights in discrete time.
problem Optimal hedging for claims with random weights in discrete time.
method Explicit recursive representation of optimal hedging strategy, without ND condition.
result Obtained explicit optimal hedging strategy in a recursive form.
A new algorithm solves constrained optimization problems with stochastic gradients.
problem Nonlinear equality constrained optimization with rank-deficient Jacobians.
method Step decomposition strategy combining normal and tangential steps.
result Convergence guarantees in rank-deficient Jacobian cases.
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …
New method solves constrained stochastic optimization problems efficiently.
problem Online statistical inference of constrained stochastic nonlinear optimization problems.
method Stochastic Sequential Quadratic Programming (StoSQP) with iterative sketching solver.
result The rescaled primal-dual sequence converges to a mean-zero Gaussian distribution.
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.
Develops an online method for solving constrained optimization problems with debiasing techniques.
problem Online inference of solutions to constrained optimization problems with equality and inequality constraints.
method Stochastic Sequential Quadratic Programming (SSQP) with momentum debiasing.
result Achieves global almost-sure convergence and local asymptotic normality with optimal primal-dual limiting covariance.
New algorithm tackles stochastic optimization with inequality constraints.
problem Stochastic optimization with inequality constraints in various applications.
method Active-set stochastic sequential quadratic programming (StoSQP) with a differentiable exact augmented Lagrangian.
result Global convergence for any initialization, KKT residuals converge to zero almost surely.
This paper speeds up OCSSVM training using SMO.
problem Training One-Class Slab SVMs is slow.
method Uses updated SMO to divide large problems into smaller, analytically solvable subproblems.
result Training OCSSVMs scales better with large datasets.
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.
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.
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.
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.
Paper develops a TR-SSQP method for noisy optimization with heavy-tailed noise.
problem Optimization problems with stochastic objectives and heavy-tailed noise.
method Trust-Region Stochastic Sequential Quadratic Programming (TR-SSQP) method.
result Achieves high-probability first-order and second-order stationarity bounds for heavy-tailed noise.
We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix inequality (LMI) whose feasible points lead to convergence bounds of biased SGD. Base…
Learning to make decisions from observed data in dynamic environments remains a problem of fundamental importance in a number of fields, from artificial intelligence and robotics, to medicine and finance. This paper concerns the problem of learning control policies for unknown linear dynamical systems so as to maximize…
Study capacity constraints in continual learning with a simple model.
problem Understanding optimal resource allocation for agents with limited memory and compute resources.
method Analyzes a capacity-constrained linear-quadratic-Gaussian (LQG) sequential prediction problem and demonstrates optimal capacity allocation strategies.
result Derives a solution to the capacity-constrained LQG sequential prediction problem and shows how to optimally allocate capacity across sub-problems in the steady state.
The paper develops methods for time-varying constrained online convex optimization.
problem Time-varying loss and constraint functions in online convex optimization.
method Model-based augmented Lagrangian methods (MALM) for time-varying and delayed feedback.
result Sublinear regret and constraint violation for both time-varying and delayed feedback scenarios.
Efficient algorithm reduces control system regret to sqrt(t).
problem Control of linear quadratic systems with guaranteed anytime performance.
method Combines SDP-based framework with regularization and perturbation mechanisms.
result Achieves anytime regret of order sqrt(t) with explicit dependence on system dimensions.
QMME balances cost and speed in convex optimization.
problem Slow convergence of first-order methods and high cost of second-order methods.
method Minimizing quadratic majorants with fixed curvature at each iteration.
result QMME framework achieves sequential convergence under standard assumptions.
Diffusion approximations optimize sequential experimentation for uncertain parameters.
problem Maximizing reward from unknown parameter Θ with delayed action.
method Bayesian sequential experimentation framework, dynamic programming, diffusion asymptotics.
result Derives diffusion approximation for optimal experimentation strategy.
The paper develops efficient estimators for semi-parametric binary models in distributed computing.
problem Estimation and inference challenges in large-scale data under non-smooth objective functions.
method Proposes one-shot and multi-round divide-and-conquer estimators with adaptive kernel smoothing to relax constraints and achieve superlinear optimization error.
result Establishes quadratic convergence up to optimal statistical error rate and handles dataset heterogeneity and high-dimensional sparse parameters.
New method for online inference of constrained optimization problems.
problem Online inference of constrained stochastic optimization problems.
method Random scaling of Sketched Stochastic Sequential Quadratic Programming (SSQP).
result Asymptotically valid confidence intervals and matrix-free computation.
Study aims to optimize financial investments by balancing risk and reward efficiently.
problem Balancing risk and reward in dynamic financial investments.
method Proposes a reinforcement learning method to maximize expected quadratic utility, focusing on first and second moments of rewards.
result The proposed method yields MV-efficient policies that maximize expected reward without increasing variance.
Improved learning algorithm for first-price auctions reduces regret significantly.
problem Challenges in learning optimal bidding strategies for first-price auctions.
method Introduced novel ideas to achieve lower regret in sequential learning.
result Achieved log2(T) regret when opponents' bid distribution is known, and T1/3+ε regret in learning case. Reinforcement Learning algorithms have recently been proposed to learn time-sequential control policies in the field of autonomous driving. Direct applications of Reinforcement Learning algorithms with discrete action space will yield unsatisfactory results at the operational level of driving where continuous control a…
RL agent outperforms model-based approach in detecting price manipulation.
problem Detecting and exploiting price manipulation opportunities.
method Compared model-free RL with model-based approach in a market with Almgren-Chriss framework.
result RL consistently outperforms model-based approach, especially with noisy parameter estimates.
Python package for projecting onto quadratic hypersurfaces.
problem Projections onto non-cylindrical central quadratic hypersurfaces.
method User-friendly Python package with documentation.
result Efficiently projects points onto quadratic hypersurfaces.
Algorithm detects changes online using expert tracking.
problem Online change point detection in nonparametric settings.
method Sequential score function estimation and tracking the best expert approach.
result Algorithm performs well in artificial and real-world data.
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization techniques, that heavily rely on heuristics for regularization in order to achi…
This paper shows how to combine optimal tests into log-optimal processes.
problem How to combine optimal sequential tests into log-optimal processes.
method Using a new class of WAIT e-processes, the paper aggregates asymptotically optimal sequential tests into asymptotically log-optimal processes.
result It is possible to aggregate asymptotically optimal sequential tests into asymptotically log-optimal e-processes.
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimiz…
The paper studies optimal transport in linear quadratic systems and derives interpolation inequalities.
problem Optimal transport problem in Linear Quadratic optimal control systems.
method Well-posedness of the Monge problem, regularity of optimal transport map, displacement interpolation of measures.
result Derivation of general interpolation inequalities for entropy functionals.
Framework learns continuous dynamics from sparse trajectories.
problem Learning dynamics from sparsely sampled and high-dimensional trajectories.
method Interpolative Multi-Marginal Flow Matching (IMMFM) framework.
result IMMFM outperforms existing methods in forecasting and downstream tasks.
Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.
problem Optimal unimodal transformation of univariate model scores under linear loss functions.
method Proposes a sequential approach to estimate the optimal rectangular fit for observed samples with each new sample.
result Sequential approach achieves optimal efficiency with logarithmic time complexity per iteration.
This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated …
Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
In this paper, a new sequential surrogate-based optimization (SSBO) algorithm is developed, which aims to improve the global search ability and local search efficiency for the global optimization of expensive black-box models. The proposed method involves three basic sub-criteria to infill new samples asynchronously to…
New method calibrates false detection rates in sequential change detection.
problem Challenges in setting time-invariant thresholds for false positives.
method Simulation-based approach to time-varying thresholds.
result Accurately targets desired expected runtime while keeping false positive rate constant.
We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data, proposed by Brunton et al., followed by performance of LASSO for this purpose. …
In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of the updates for the linear regression problem and show that there is a one-to-one …
Novel approximation hierarchy for sparse quadratic programs.
problem Sparse Quadratic Programs with Cardinality Constraints.
method Exploits rank-dominating eigenvectors for min-max optimization over binary variables.
result Efficient screening of nonzero elements with scalable optimization algorithms.
Abstract perspective on quadratic programming for optimal portfolio allocation.
problem Optimal allocation problems in long portfolio theory.
method Using maximum principles and distinguished boundaries in reproducing kernel Hilbert spaces.
result Support of an optimal distribution lies in a variety intersecting a distinguished boundary.
Optimal sequential testing for Markovian data with lower and upper bounds.
problem Sequential hypothesis testing for Markovian data.
method Non-asymptotic lower bounds and optimal test design.
result Optimal test matches lower bound asymptotically.
Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis. In a quest to lower teaching complexity and to achieve more natural teacher-learner interactions, several teaching models and complexity measures have b…
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…
Optimized parallel algorithms for identifying strong ties in data.
problem Identifying strong ties in data with varying distances and community sizes.
method Design and analysis of sequential and parallel algorithms for partitioned local depths.
result Optimized algorithms achieve up to 19.4x speedup in parallel execution.
Paper presents an ADMM-based approach to efficiently integrate quadratic programming layers into neural networks.
problem Integrating quadratic programs into neural networks for optimization.
method An ADMM-based network layer architecture for solving quadratic programs efficiently.
result The ADMM layer is approximately an order of magnitude faster than existing methods for medium scaled problems.