Convex program for estimating nonlinear recurrent models with stability conditions.
problem Estimating parameters in nonlinear recurrent models with stability conditions.
method Formulated a convex program for the estimator of nonlinear recurrent models under stability conditions.
result Sample complexity for the convex program estimator under stable dynamics.
Geometric programming approach for traffic equilibrium problems.
problem Optimizing traffic equilibrium in transportation systems.
method Finslerian dynamical model for nonlinear complementarity problems.
result Effective solution for various equilibrium problems in transportation.
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.
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…
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…
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
Proposes PKM for soft K-means clustering.
problem Soft K-means (m=1) unsolved since 1981.
method Probabilistic K-Means (PKM) via nonlinear programming.
result Proposed methods solve PKM efficiently.
Method approximates efficient frontier of chance-constrained programs.
problem Approximating the efficient frontier of chance-constrained nonlinear programs.
method Stochastic approximation method based on bi-objective viewpoint.
result Converges to stationary solutions of a smooth approximation of the original problem.
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.
Bayesian framework for robust model discovery from noisy data.
problem Robust model discovery from noisy, sparse and irregular observations of nonlinear systems.
method Bayesian differential programming using Hamiltonian Monte Carlo and sparsity-promoting priors.
result Efficient inference of posterior distributions over plausible models with quantified uncertainty.
We discuss some of the key ideas of Perelman's proof of Poincaré's conjecture via the Hamilton program of using the Ricci flow, from the perspective of the modern theory of nonlinear partial differential equations.
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationar…
The paper optimizes portfolios to minimize drawdown, outperforming market indices.
problem Minimizing drawdown in financial portfolios.
method Formulated as a nonlinear program, partially linearized, solved using SCIP.
result Minimal drawdown portfolios outperform market indices in return, Sharpe ratio, maximum and average drawdown.
Recently, a novel adaptive wave model for financial option pricing has been proposed in the form of adaptive nonlinear Schrödinger (NLS) equation [Ivancevic a], as a high-complexity alternative to the linear Black-Scholes-Merton model [Black-Scholes-Merton]. Its quantum-mechanical basis has been elaborated in [Ivancevi…
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.
Investment and insurance decisions are studied in a model with nonlinear portfolio frictions and background risk.
problem Investment and insurance decisions under a model with nonlinear portfolio frictions and background risk.
method Dynamic programming approach to find optimality conditions.
result Agent can choose to assume, partially assume, or purchase total insurance against adverse jumps in wealth.
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.
Neural networks enhance linear programming for complex decision-making problems.
problem High-dimensional and combinatorial operations research problems.
method Hybrid solution method combining linear programming and neural networks.
result Neural network value function approximations outperform polynomial approximations in a transportation problem.
New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.
problem Solving nonconvex optimization problems with stochastic objectives and constraints.
method Single-loop quadratic penalty and augmented Lagrangian algorithms with variance reduction techniques.
result Achieved best-known complexity guarantees for solving nonconvex optimization problems with stochastic objectives and constraints.
This work shows how to compute subderivatives efficiently without errors.
problem Inefficient and incorrect computation of subderivatives in ML libraries.
method Developed a method to compute provably correct generalized subderivatives at a cost close to the function itself.
result Provable correct generalized subderivatives can be computed at a cost within a factor of 6 of the function itself.
Hedging in the presence of transaction costs leads to complex optimization problems. These problems typically lack closed-form solutions, and their implementation relies on numerical methods that provide hedging strategies for specific parameter values. In this paper we use a genetic programming algorithm to derive exp…
The paper tackles energy management in buildings with PCM using dynamic programming.
problem Optimal scheduling of HVAC systems in buildings with PCM is challenging due to nonlinear and non-convex characteristics.
method The paper uses dynamic programming to address the nonlinear nature of PCM, incorporating macro actions and multi-time scale Markov decision processes to reduce computational burden.
result The proposed method demonstrates a computational speed-up of up to 12,900 times compared to direct DP application.
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 k4p. 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…
Novel algorithm for optimal control of nonlinear systems.
problem Optimal control of nonlinear stochastic dynamical systems with unknown dynamics.
method Decoupled data-based approach combining open-loop and closed-loop control.
result Performance of D2C algorithm is approximately optimal and significantly reduces training time.
We consider the question of estimating a solution to a system of equations that involve convex nonlinearities, a problem that is common in machine learning and signal processing. Because of these nonlinearities, conventional estimators based on empirical risk minimization generally involve solving a non-convex optimiza…
We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dyn…
Develops new optimization techniques for decision-making under uncertainty.
problem Decision-making under uncertainty with complex cost functions and nested expectations.
method Introduces Multistage Conditional Compositional Optimization (MCCO) and develops multilevel Monte Carlo techniques.
result New optimization techniques reduce scenario complexity from exponential to polynomial growth.
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.
Checks difference flatness via involutive distributions.
problem Nonlinear discrete-time system flatness testing.
method Computing a sequence of involutive distributions.
result Efficient implementation in computer algebra.
VNA solves large portfolio optimization problems efficiently.
problem Large-scale portfolio optimization under real-world constraints.
method Mapped to Ising-like Hamiltonian and solved with VNA.
result Identifies near-optimal solutions for over 2,000 assets.
New method tackles nonlinear, infinite-dimensional signal processing problems.
problem Nonlinear, infinite-dimensional signal processing challenges.
method Directly addresses continuous, nonlinear problems as sparse functional optimization.
result Proves no duality gap for non-atomic problems, allowing efficient solution.
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalisations of the…
This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm …
Paper proposes a method for optimizing local policies for trajectory-centric reinforcement learning.
problem Challenges in global policy optimization for non-linear systems and poor performance of open-loop trajectory optimization.
method Formulates trajectory optimization and local policy synthesis as a single optimization problem and solves it as a nonlinear programming instance.
result Demonstrates improved performance of the proposed technique under simplifying assumptions.
We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with Sequential Monte Carlo, this automatically yields improvements such as locally-optimal pr…
Paper characterizes optimal learning trajectories for high-dimensional nonlinear models.
problem Characterizing optimal learning trajectories in high-dimensional nonlinear models.
method Exploits maximum principle and dynamic programming for an optimal control problem of a gradient system.
result Constructs optimal learning trajectories leading to optimal model parameters.
Study optimal investment and consumption strategies with various transaction costs.
problem Investment and consumption decisions under varying transaction costs.
method Dynamic programming and singular perturbation expansion for small cost-to-wealth ratio.
result Derive leading-order asymptotic formulas for no-trade regions and trading boundaries.
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …
Optimizes marketing strategies with practical constraints.
problem Adjusting marketing activities with minimum and maximum changes.
method Formulated as a mixed integer nonlinear program (MINLP), reformulated for computational efficiency.
result Significant improvements in solution process for realistic problems.
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma approximation is employed to overcome it. Thus, the optimization problem is reduced to a we…
Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and state-space models still scales poorly; each MCMC transition takes linear time i…
We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected execution cost. We find that the optimal solution is front loaded for co…
JAXFit speeds up curve fitting on GPUs.
problem Nonlinear least squares curve fitting problems.
method Trust region method on GPU with automatic differentiation.
result Significantly faster than CPU and other GPU libraries.
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.
This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one…
Optimal Control Theory optimizes neural networks, improving robustness and efficiency.
problem Optimizing deep neural networks (DNNs) for better performance and efficiency.
method Integrating Optimal Control Theory with Backpropagation to develop a new optimizer.
result Optimal Control Theoretic Neural Optimizer (OCNOpt) improves upon existing methods in robustness and efficiency.
CEFOL uses deep learning for dynamic programming with recursive utility.
problem Challenges in solving dynamic programming problems with recursive utility.
method Introduces a separate neural network for certainty equivalent, uses first-order optimality conditions to learn value and policy functions.
result CEFOL achieves high accuracy in learning value and policy functions, matching VFI benchmarks.