Study uses machine learning to recommend best solvers for slab transport problems.
problem Auto-selecting the best solvers for transport problems in uniform slabs.
method Three solvers (Richardson, diffusion synthetic acceleration, nonlinear diffusion acceleration) and five machine learning algorithms (linear discriminant analysis, K-nearest neighbors, support vector machine, random forest, neural networks) were tested.
result Random forest and K-nearest neighbors showed potential as best solvers for classification problems.
Recommender systems play an essential role in the modern business world. They recommend favorable items like books, movies, and search queries to users based on their past preferences. Applying similar ideas and techniques to Monte Carlo simulations of physical systems boosts their efficiency without sacrificing accura…
The majority of recommender systems are designed to recommend items (such as movies and products) to users. We focus on the problem of recommending buyers to sellers which comes with new challenges: (1) constraints on the number of recommendations buyers are part of before they become overwhelmed, (2) constraints on th…
BanditLP optimizes personalized recommendations for large-scale systems.
problem Optimizing personalized recommendations for large-scale systems with constraints.
method Unified neural Thompson Sampling for learning and large-scale linear programming for action selection.
result Consistent gains over strong baselines in experiments and business win in LinkedIn's email marketing system.
PMD measures user distances using optimal transportation, improving recommendation accuracy.
problem Sparse data and lack of co-rated items in collaborative filtering.
method PMD is an Earth Mover's Distance-based user distance measure that utilizes all ratings.
result PMD achieves superior recommendation accuracy, especially in sparse data scenarios.
In this paper, we solve portfolio rebalancing problem when security returns are represented by uncertain variables considering transaction costs. The performance of the proposed model is studied using constant-proportion portfolio insurance (CPPI) as rebalancing strategy. Numerical results showed that uncertain paramet…
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
problem Slow convergence of Krylov subspace solvers for ill-conditioned matrices.
method Graph neural surrogate and Bayesian optimization for AI-tuned MCMC parameters.
result 50% reduction in iterations to convergence on unseen system.
This paper optimizes PCE for efficient surrogate modeling in engineering.
problem Efficiently selecting polynomial regressors for surrogate modeling in computationally expensive models.
method Three state-of-the-art basis-adaptive sparse PCE methods are compared and analyzed.
result Automatic selection of the best solver and basis-adaptive scheme improves surrogate model accuracy.
Ranking items to be recommended to users is one of the main problems in large scale social media applications. This problem can be set up as a multi-objective optimization problem to allow for trading off multiple, potentially conflicting objectives (that are driven by those items) against each other. Most previous app…
Exact solver speeds up Weston-Watkins SVM subproblem significantly.
problem Improving performance of Weston-Watkins multiclass SVM.
method Novel reparametrization for exact subproblem solving.
result Significant speed-up over state-of-the-art solvers for large number of classes.
Optimizes neural networks with blackbox solvers using Time-cost Regularization.
problem Improving neural network performance by integrating efficient solvers for complex problems.
method Optimizes both the primary loss function and the performance of the blackbox solver using Time-cost Regularization. Introduces a hyper-blackbox concept to learn blackbox parameters.
result Significant improvement in neural network performance through optimization of blackbox solvers.
Study analyzes 3,171 stocks to pick efficient portfolios using quantum and classical solvers.
problem Creating efficient stock portfolios from a large dataset.
method Used classical and quantum solvers to optimize portfolios of 3,171 US stocks.
result Demonstrated the effectiveness of quantum and classical solvers in portfolio optimization.
The paper speeds up hyperparameter optimisation in Gaussian processes.
problem Scaling hyperparameter optimisation to large datasets.
method Improvements to linear system solvers (pathwise gradient, warm starting, early stopping).
result Speed-ups of up to 72x and residual norm decreases of up to 7x.
New solver MPLP++ outperforms existing solvers for dense graph models.
problem Efficiently solving dense, discrete Graphical Models with pairwise potentials.
method Dual Block-Coordinate Ascent with MPLP++ modification.
result MPLP++ significantly outperforms existing solvers, including TRWS.
CRA improves UL-based CO solvers by dynamically smoothing and enforcing discreteness.
problem Local optima and artificial rounding issues in UL-based CO solvers.
method Continuous Relaxation Annealing (CRA) strategy that dynamically shifts from continuous to discrete solutions.
result Significantly enhances UL-based CO solver performance and eliminates artificial rounding.
Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesia…
Study compares 5 ODE solvers on 3 case studies, finding varying accuracy.
problem Comparing estimation accuracy of 5 ODE solvers on 3 case studies.
method Used 5 different numerical ODE solvers (Euler's, Heun's, Midpoint, Runge-Kutta 4th order, ODE45) on 3 case studies and compared their results.
result Different solvers have varying accuracy depending on the case study.
A new method combines classical and machine learning PDE solvers efficiently.
problem Combining classical and machine learning PDE solvers to reduce computational cost and improve accuracy.
method Proposes an approximate greedy router to select solvers at each iteration, mimicking a greedy approach.
result Consistently reduces final error and AUC of the error trajectory compared to single-solver baselines and hybrid approaches.
Higher-order ODE solvers improve deep learning performance.
problem Improving deep learning performance using higher-order ODE solvers.
method Evaluation and improvement of Runge-Kutta (RK) methods for deep learning.
result Higher-order RK solvers can improve deep learning performance by incorporating key ingredients of optimizers.
SA-Solver improves stochastic sampling from DPMs.
problem Efficient sampling from Diffusion Probabilistic Models (DPMs) is time-consuming.
method Proposes SA-Solver, an improved stochastic Adams method for solving diffusion SDE.
result SA-Solver achieves improved or comparable performance compared to SOTA methods for few-step sampling.
Accelerates data generation in score-based models.
problem Slow generation of realistic data by score-based models.
method Developed an adaptive step size SDE solver.
result Generates data 2-10 times faster with high quality.
New deep learning solver for high-dimensional derivative pricing.
problem High-dimensional derivatives pricing problems.
method Combines deep learning with least square regression for backward SDE solving.
result Accurate and efficient pricing of complex derivatives.
Although optimization is the longstanding algorithmic backbone of machine learning, new models still require the time-consuming implementation of new solvers. As a result, there are thousands of implementations of optimization algorithms for machine learning problems. A natural question is, if it is always necessary to…
New taxonomy and improved solvers for discrete energy minimization.
problem Maximum-a-posteriori inference in discrete graphical models.
method Dual block-coordinate ascent rule, theoretical analysis, new solver variants.
result Improved state-of-the-art solver outperforming existing methods on all test instances.
End-to-end trainable graph matching using improved combinatorial solvers.
problem Graph matching in deep learning.
method Combining deep learning with optimized combinatorial solvers.
result Advances state-of-the-art on deep graph matching benchmarks.
MIP-GNN uses graph neural networks to predict variable biases for MIP solvers.
problem Improving combinatorial optimization through data-driven insights.
method Encoding MILP interactions as graphs, training a graph neural network to predict variable biases, and guiding the MIP solver with these predictions.
result Significant improvements in solving binary MILPs compared to default settings of state-of-the-art solvers.
Developing stable and scalable probabilistic ODE solvers for stiff and high-dimensional problems.
problem Stiff and high-dimensional ODEs
method Matrix-free update step and iterative re-linearization
result Improved stability and scalability
DPM-Solver speeds up DPM sampling to 10-20 function evaluations.
problem Slow sampling from Diffusion Probabilistic Models (DPMs).
method Exact formulation of diffusion ODE solutions, using change-of-variable and exponentially weighted integral.
result Generates high-quality samples in 10-20 function evaluations.
The paper improves ODE solvers by integrating diverse information types.
problem Improving accuracy and physical meaningfulness of ODE solutions.
method Leveraging probabilistic solvers to include second-order information and physical conservation laws.
result Solutions become more accurate and physically meaningful with additional information.
Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.
problem Efficiently solving ordinary differential equations (ODEs) with reduced computational cost.
method Formulated a parallel-in-time probabilistic numerical ODE solver using time-parallel formulation of iterated extended Kalman smoothers.
result Reduces span cost from linear to logarithmic in the number of time steps.
Ada-LISTA adapts neural solvers for varying models.
problem Adapting neural solvers for varying models.
method Ada-LISTA receives pairs of signals and dictionaries, learns a universal architecture, and solves sparse coding in linear rate.
result Ada-LISTA solves sparse coding in linear rate for varying models.
ML4CO uses machine learning to improve combinatorial optimization solvers.
problem Solving combinatorial problems in practice often involves related data distributions.
method Replacing heuristic components with machine learning approaches.
result Improved state-of-the-art combinatorial optimization solvers.
New ODE solvers improve training efficiency and accuracy.
problem Training Neural ODEs requires efficient and accurate gradient calculation.
method Presented algebraically reversible ODE solvers that are time and memory efficient, calculate exact gradients, and are numerically stable.
result Reversible solvers strictly improve upon previous architectures in efficiency and accuracy.
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be sub-optimal for specific classes of problems. In contrast to existing hand-craft…
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…
GENIE accelerates DDM synthesis with higher-order solvers.
problem Efficiently solving the differential equation for high-quality generation.
method Higher-order Taylor methods, utilizing Jacobian-vector products.
result GENIE significantly accelerates synthesis compared to previous solvers.
New solver avoids memory issues for long differential equations.
problem Memory constraints in adaptive probabilistic ODE solvers.
method Fixed memory demands adaptive probabilistic solver using robust state estimation.
result Eliminates memory issues for long time series simulations.
skscope simplifies sparsity-constrained optimization in Python.
problem Tedious mathematical deduction and programming for sparsity-constrained optimization.
method Introduces skscope, a Python library that allows users to solve sparsity-constrained optimization problems by just programming the objective function.
result skscope enables state-of-the-art solvers to quickly attain sparse solutions in high-dimensional spaces, achieving up to 80x speedup.
C-ADAM is a new adaptive solver for complex nested problems.
problem Solving compositional problems involving nested expected values.
method Adaptive solver for non-linear functional nesting of expected values.
result C-ADAM converges to a stationary point in O(δ−2.25). Novel probabilistic solver speeds up solving related linear systems.
problem Efficiently solving multiple related linear systems.
method Probabilistic linear solver over the parameter space, leveraging solved systems.
result Faster and more efficient solution of related linear systems.
Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of classic regression solvers. We show that SGD schemes efficiently track the true s…
This work introduces a new loss function to improve the efficiency of optimization-based PDE solvers.
problem Optimization-based PDE solvers converge slowly and are inefficient compared to classical iterative solvers.
method Proposes a novel Stabilized Gradient Residual (SGR) loss function to modulate the condition number.
result The SGR loss achieves orders-of-magnitude faster convergence than the MSE loss in both ODIL and PINNs frameworks.
Machine learning speeds up GPR simulations.
problem Computational demands of simulating practical GPR problems.
method Automatic ML-based forward solver framework using gprMax.
result Near-real-time GPR simulations achieved.
ThiopheneIV is a new solver for implied volatility with proven monotonicity.
problem Efficiently solving implied volatility in financial models.
method Monotone core with Euler-Chebyshev and Halley steps, exact arithmetic proof, practical boundary handling.
result ThiopheneIV agrees closely with multiprecision Black reference prices at low latency.
New framework for probabilistic linear solvers reduces manual effort.
problem Manual implementation of probabilistic iterative methods is laborious.
method Affine Tracing: Automatically constructs PIMs from standard implementations.
result Any realistic affine PIM is calibrated, motivating their adoption.
Study evaluates Deep PDE solvers for high-dimensional option pricing, identifying key sources of error.
problem Empirical study on error analysis of Deep PDE solvers for high-dimensional option pricing.
method Comparative experiments with Deep BSDE method and other solvers, identifying three main sources of error.
result Deep BSDE method is superior and robust to option specifications, improving with larger batch sizes and fewer time steps.
Leveraging on the convexity of the Lasso problem , screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying relevant variables, several non-convex regularizers for the Lasso have been prop…
Calibrated probabilistic solvers improve accuracy of ODE estimates.
problem Uncertainty in probabilistic ODE solutions is not well-calibrated for adaptive step sizes.
method Introduce and assess several calibration methods for probabilistic ODE solvers.
result Calibration methods interact efficiently with adaptive step-size selection, improving posteriors.