Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we must often compute expected downstream values corresponding to current decision…
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48 results for “Approximate Linear Programs”
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be used as a black box to speed up linear programming solvers dramatically, by two…
Solving linear programs by using entropic penalization has recently attracted new interest in the optimization community, since this strategy forms the basis for the fastest-known algorithms for the optimal transport problem, with many applications in modern large-scale machine learning. Crucial to these applications h…
Recently, Petrik et al. demonstrated that L1Regularized Approximate Linear Programming (RALP) could produce value functions and policies which compared favorably to established linear value function approximation techniques like LSPI. RALP's success primarily stems from the ability to solve the feature selection and va…
New method for optimistic planning in MDPs using regularization.
problem Optimistic planning in infinite-horizon discounted MDPs.
method Regularized dynamic programming for approximate value iteration.
result Achieves near-optimal statistical guarantees in learning policies.
This paper introduces a new technique for quantifying the approximation error of a broad class of probabilistic inference programs, including ones based on both variational and Monte Carlo approaches. The key idea is to derive a subjective bound on the symmetrized KL divergence between the distribution achieved by an a…
SurvLIME-Inf simplifies explanation of survival models using a linear programming approach.
problem Explain complex survival models using simple linear programming.
method Uses -norm for feature importance and explains black-box models.
result SurvLIME-Inf outperforms SurvLIME in small training set scenarios.
New methods improve solving linear systems and preconditioning with reduced complexity.
problem Efficiently solving linear systems and preconditioning matrices.
method Developed structured semidefinite programming algorithms.
result Improved runtimes for preconditioning and solving linear systems.
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, wi…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…
New method for natural policy gradients converges linearly.
problem Improving natural policy gradient methods for better convergence.
method Fisher-Rao gradient flow applied to state-action distributions.
result Linear convergence rate with geometry-dependent factor.
This research optimizes Andrews plots for better visual clarity in high-dimensional data.
problem Visualizing high-dimensional datasets with clarity and aesthetics.
method Developed a method to add spectral smoothing to Andrews plots to reduce visual clutter.
result Optimal spatial-spectral smoothing leads to more aesthetically pleasing and clutter-free visualizations.
Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficul…
Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently, by solving an integer linear program. Because of the complex scoring functions …
Self-guided ALPs improve MDP policies without domain knowledge.
problem Improving MDP policies with minimal domain knowledge.
method Self-guided sequence of ALPs with random basis functions and state-relevance distribution.
result High probability error bounds and improved policy performance.
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 .
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are mostly not scalable. In this paper, we develop a method that transforms the quadra…
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…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant extension of the "anchored regression" method formulated and analyzed in [10] f…
SOC-ICNN expands neural network representational capacity by using conic optimization.
problem Restrictive representational capacity of ReLU-based ICNNs.
method Proposes SOC-ICNN architecture that uses Second-Order Cone Programming.
result SOC-ICNN strictly expands representational space without increasing complexity.
Develops a fair clustering algorithm for datasets with outliers.
problem Fair clustering with outliers in datasets.
method Solves a linear program to identify and exclude outliers, then applies a rounding algorithm to find fair centers.
result Guaranteed approximation of fair radius and clustering cost.
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.
New algorithm tackles dynamic assortment optimization with knapsack constraints.
problem Optimizing retailer's assortment decisions under resource constraints with multi-nomial choice modeling.
method Epoch-based re-solving algorithm that transforms MNL's fractional structure into a linear program with slack variables.
result Regret scales logarithmically with time horizon and resource capacities.
Framework learns linear programs from optimal decisions.
problem Learning linear programs from optimal decisions is challenging.
method Gradient-based framework for learning linear programs from optimal decisions.
result Successfully learns linear programs and multi-commodity flow instances.
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…
Approximate dynamic programming algorithms, such as approximate value iteration, have been successfully applied to many complex reinforcement learning tasks, and a better approximate dynamic programming algorithm is expected to further extend the applicability of reinforcement learning to various tasks. In this paper w…
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…
Study optimal policies under budget and coverage constraints.
problem Optimal policy learning with budget and coverage constraints.
method Combination of knapsack structure, affine threshold rule, linear programming relaxation, Greedy-Lagrangian (GLC), and rank-and-cut (RC) algorithms.
result GLC closely approximates the optimal solution and achieves near-optimal performance in finite samples; RC is approximately optimal under certain conditions.
FVI method calculates bicausal OT with neural networks, outperforming other methods.
problem Computing bicausal optimal transport with adapted coupling structures.
method FVI method using multilayer neural networks to approximate value functions.
result FVI method outperforms linear programming and Sinkhorn methods in scalability.
Deep learning solves dynamic programming with recursive utility.
problem Challenges in solving high-dimensional discrete-time dynamic programming problems with recursive utility.
method Certainty Equivalent Learning (CEL) algorithm that learns certainty-equivalent value directly with neural networks.
result Accurate value and policy approximations in high-dimensional problems, comparable to VFI in some cases.
I show that every rectifiable simple closed curve in the plane can be continuously deformed into a convex curve in a motion which preserves arc length and does not decrease the Euclidean distance between any pair of points on the curve. This result is obtained by approximating the curve with polygons and invoking the r…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine learning applications and theoretical approximation algorithms for graph cluste…
Study bounds financial path expectations using martingale distributions.
problem Bounding path-dependent financial expectations over martingale distributions.
method Relaxed martingale optimal transport problem, approximated via linear programming.
result Empirical relaxation can be approximated within O(n^(-1/2)) error.
Combines dynamic programming and neural networks for optimal portfolio execution in regime-switching markets.
problem Optimal execution in a market with multiple regimes and non-linear impact costs.
method Four-step numerical framework: approximated orthogonal portfolios, dynamic program for schedule, neural network optimization.
result Neural network optimized strategy outperforms traditional methods in both CRRA and mean-variance objectives.
Recent work in model-agnostic explanations of black-box machine learning has demonstrated that interpretability of complex models does not have to come at the cost of accuracy or model flexibility. However, it is not clear what kind of explanations, such as linear models, decision trees, and rule lists, are the appropr…
We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear programming problems. Subsequently approximating those systems by finite dimensional …
An analysis of linear regression and neural networks approximation for the pricing of swing optionsq-fin.MF
This paper compares linear regression and neural networks for pricing swing options.
problem Pricing swing options using approximation methods.
method Linear regression and neural networks for approximating the continuation value and swing price.
result The approximation methods converge to the actual swing price as the number of functions or Monte Carlo samples increases.
New method uses DC functions for piecewise linear regression.
problem Regression with piecewise linear constraints.
method Estimates piecewise linear convex functions using a difference of convex functions.
result Method achieves close to minimax statistical risk and comparable performance to existing methods.
Differential privacy enables organizations to collect accurate aggregates over sensitive data with strong, rigorous guarantees on individuals' privacy. Previous work has found that under differential privacy, computing multiple correlated aggregates as a batch, using an appropriate \emph{strategy}, may yield higher acc…
Bayesian optimization tackles non-convex, two-stage stochastic problems efficiently.
problem Solving non-convex, two-stage stochastic optimization problems with expensive, black-box evaluations.
method Knowledge-gradient-based acquisition function for joint optimization of first- and second-stage variables.
result Comparable and superior empirical results compared to alternatives.
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.
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of dimensionality by minimizing a pessimistic bound on the policy loss. This approach tur…
Unified approach for optimizing predictions in linear programming and inverse problems.
problem Optimizing predictions in linear programming and inverse problems.
method Maximum optimality margin approach.
result Unified approach that balances computational efficiency and theoretical properties.
Quantile Temporal-Difference learning proved convergent with proof.
problem Lack of theoretical understanding of QTD despite empirical success.
method Proof of convergence using stochastic approximation and non-smooth analysis.
result QTD converges to fixed points with probability 1.
We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, e.g., in non-linear option pricing problems or in probabilistic dis…
Paper introduces -DER for regression tasks using morphological operators and convex-concave procedure.
problem Developing a universal approximator for regression tasks.
method Introduces -DER model, trains it using a convex-concave procedure (CCP) to minimize least-squares.
result Outperforms other hybrid morphological models and state-of-the-art approaches.
Physarum-inspired solver speeds up LP solving in neural networks.
problem Efficiently solving linear programming problems within neural networks.
method Inspired by Physarum dynamics, a differentiable solver for LPs.
result Solver outperforms existing methods in video segmentation and few-shot learning.
We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to infinity, the upper hedging price of a European option converges to the solution of…