In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a convex programming pro…
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48 results for “sequential convex programming”
New method finds arbitrage opportunities in fluctuating asset bands.
problem Finding arbitrage opportunities in fluctuating asset bands.
method Formulate as maximizing volatility within a price band, using convex-concave optimization.
result Approximately solves non-convex optimization problem for moving-band arbitrage.
New method solves complex constrained optimization problems.
problem Constrained nonconvex-nonconcave minimax optimization problems.
method Inexact proximal gradient method using sequential convex programming.
result Established complexity guarantees for approximate stationary points.
Adaptive SAA solves large-scale stochastic linear programs efficiently.
problem Solving large-scale two-stage stochastic linear programs.
method Iterative algorithm with adaptive sample size and warm starts.
result The algorithm converges to the true solution set with a probabilistic guarantee.
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimat…
Paper uses integer programming for non-convex boosting in classification.
problem Improving classification performance using non-convex optimization.
method Non-convex boosting via integer programming.
result Results comparable to or better than state-of-the-art.
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.
Extends DCP framework to Hadamard manifolds for geodesically convex functions.
problem Verifying convexity in nonlinear programs on Hadamard manifolds.
method Introduces Disciplined Geodesically Convex Programming (DGCP) framework, defining compositions and transformations for geodesically convex functions.
result Allows verification of geodesic convexity for a broader range of functions, including statistical estimators and matrix-valued optimization.
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…
This article presents the use of Answer Set Programming (ASP) to mine sequential patterns. ASP is a high-level declarative logic programming paradigm for high level encoding combinatorial and optimization problem solving as well as knowledge representation and reasoning. Thus, ASP is a good candidate for implementing p…
New tighter confidence bounds for sequential kernel regression.
problem Quantifying uncertainty in sequential learning algorithms.
method Martingale tail inequalities and conic programming.
result New confidence bounds are tighter than existing ones.
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's metho…
We consider discriminative dictionary learning in a distributed online setting, where a network of agents aims to learn a common set of dictionary elements of a feature space and model parameters while sequentially receiving observations. We formulate this problem as a distributed stochastic program with a non-convex o…
Most of Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) algorithms in existing probabilistic programming systems suboptimally use only model priors as proposal distributions. In this work, we describe an approach for training a discriminative model, namely a neural network, in order to approximate the …
Programming has been an important skill for researchers and practitioners in computer science and other related areas. To learn basic programing skills, a long-time systematic training is usually required for beginners. According to a recent market report, the computer software market is expected to continue expanding …
Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid…
Paper presents algorithm for optimal job selection with dynamic scoring.
problem Optimal job assignment in a sequential selection process with dynamic scores.
method Developed using dynamic programming, with extensions for partial and no-information cases.
result Algorithm allows for optimal job assignment with limited information.
The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new strategies for the optimal design of sequential experiments. First, we rigorously formul…
Forward inference techniques such as sequential Monte Carlo and particle Markov chain Monte Carlo for probabilistic programming can be implemented in any programming language by creative use of standardized operating system functionality including processes, forking, mutexes, and shared memory. Exploiting this we have …
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.
In this work, we explore how probabilistic programs can be used to represent policies in sequential decision problems. In this formulation, a probabilistic program is a black-box stochastic simulator for both the problem domain and the agent. We relate classic policy gradient techniques to recently introduced black-box…
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.
Models of complex systems are often formalized as sequential software simulators: computationally intensive programs that iteratively build up probable system configurations given parameters and initial conditions. These simulators enable modelers to capture effects that are difficult to characterize analytically or su…
Convex message passing algorithms converge to a fixed point.
problem Understanding convergence properties of convex message passing methods.
method Proving convergence of coordinate descent applied to piecewise-affine convex objectives, and showing this applies to various message passing methods.
result The iterates converge to a fixed point of the method, and the algorithm terminates in a known number of iterations.
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search step (gradient descent or Quasi-Newton iteration) into these uniformly optimal conv…
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.
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.
Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small rank despite of having a large state space, meaning that the system admits a low-d…
Unified technique for sequential estimation of convex divergences.
problem Estimating convex divergences between distributions.
method Martingale methods and maximal inequalities for reverse submartingales.
result Valid time-uniform confidence sequences for arbitrary stopping times.
In this paper we consider regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving regularized box constrained convex programming. We show that the sequence generated by these methods converges to a local minimizer.…
This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in this family. Previous online optimization methods are designed to have a total a…
Efficiently samples sequences without replacement for machine learning models.
problem Generating diverse outputs from sequential models without duplicates.
method Incremental sampling procedure for randomized programs, including neural models.
result Efficacy and flexibility of incremental sampling for large output spaces.
Convex optimization refines neural network training, improving model performance and reducing hyperparameter sensitivity.
problem Training deep neural networks using non-convex optimization methods often leads to suboptimal solutions and requires extensive tuning.
method Formulate neural network training as convex programs with regularization terms, leveraging sparse recovery models and semi-infinite programming theory.
result Convex models can achieve global optima and outperform traditional non-convex methods, with improved robustness to hyperparameters.
Develops methods for finding counterfactual explanations in sequential decision making.
problem Finding counterfactual explanations for sequential decision making processes.
method Formal characterization of sequential actions and states using Markov decision processes and Gumbel-Max structural causal model. Introduces a polynomial time algorithm based on dynamic programming.
result Algorithm finds optimal counterfactual explanations for sequential decision making.
Efficiently selects top-m designs for various contexts using sequential sampling.
problem Optimizing selection of top-m designs across different contexts.
method Formulated as a stochastic dynamic programming problem, developed sequential sampling policy.
result Asymptotically optimal sampling ratios for efficient selection.
Neural networks solve copositive programs, revealing insights into training problems.
problem Training two-layer vector-output ReLU neural networks.
method Convex analysis and copositive programming.
result Neural networks solve copositive programs, providing insights into training problems.
Exact simulation of correlated binary outcomes using PMF constraints and linear programming.
problem Simulating dependent Bernoulli outcomes with specific means and correlations.
method Formulate the problem over the joint Bernoulli PMF, impose constraints, and solve as a linear program. Use convex-hull characterization and truncated-moment completion scheme for feasibility and simulation.
result Exact simulation framework for correlated binary outcomes, providing a convex-hull characterization and truncated-moment completion scheme.
Transformers improve solving mixed-integer programs, especially CLSP.
problem Solving Capacitated Lot Sizing Problem (CLSP) with mixed-integer programming.
method Employing transformer models to predict binary variables in CLSP.
result Transformer model outperforms CPLEX and LSTM in solving CLSP.
PClean automates Bayesian data cleaning for specific datasets.
problem Bayesian inference for diverse and complex data cleaning.
method Domain-specific probabilistic programming language with custom models and inference.
result PClean programs outperform general-purpose PPLs in accuracy and runtime.
Max-linear regression problem solved with convex programming.
problem Estimating parameters in max-linear regression models.
method Formulated and analyzed a scalable convex program called anchored regression (AR).
result AR provides high probability recovery of parameters with a sample complexity of .
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 improves online learning algorithms for LP problems, achieving better regret bounds.
problem Achieving optimal regret bounds in online linear programming.
method Develops a new framework for first-order online learning algorithms under certain error bound conditions.
result First-order learning algorithms achieve regret in continuous support and regret in finite support, improving over .
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 uses SoS densities and α-divergences for efficient sequential transport maps.
problem Efficiently generating samples from approximated densities.
method Sequential transport maps using Sum-of-Squares (SoS) densities and α-divergences.
result Convex optimization problems with efficient semidefinite programming solutions.
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate constraints or objective functions for optimization. Ensemble methods, like bagging, sm…
A new MDP with Bandits approach for sequential decision making in linear-flow scenarios.
problem Sequential decision making with limited feedback in a linear-flow context.
method Formulated as an MDP with Bandits, using Thompson sampling for action selection and exact dynamic programming for allocation.
result The proposed MDP with Bandits algorithm outperforms other methods in sequential decision making.
Maximum A posteriori Probability (MAP) inference in graphical models amounts to solving a graph-structured combinatorial optimization problem. Popular inference algorithms such as belief propagation (BP) and generalized belief propagation (GBP) are intimately related to linear programming (LP) relaxation within the She…