In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study, instead of the single optimal solution, we consider finding a set of diverse yet nea…
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48 results for “optimal solution”
A proof of imitation of Wasserstein inverse reinforcement learning for multi-objective optimizationcs.LG
Proof shows imitation of expert's reward and solutions in multi-objective optimization.
problem Multi-objective optimization with reward and solution imitation.
method Wasserstein inverse reinforcement learning.
result Wasserstein inverse reinforcement learning enables imitation of expert's reward and solutions in multi-objective optimization.
Paper proposes an efficient method to optimize neural networks without backpropagation.
problem Computational inefficiency and scalability issues in neural network optimization.
method Derives explicit solutions to optimize neural networks, reducing computational costs.
result Explicit solutions achieve near-optimality and can discover better optima than backpropagation.
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under th…
Neural network discovers exact solutions to QP with linear constraints.
problem Discovering exact solutions to Quadratic Programs (QP) with linear constraints using neural networks.
method Proposes a neural network modeling approach that analytically derives model parameters from problem coefficients, ensuring closed-form solutions without training.
result The closed-form NN model produces exact solutions for every critical region of the QP solution function, outperforming DNNs and commercial solvers in terms of optimality and feasibility.
New method optimizes portfolio weights as functions, outperforming traditional approaches.
problem Optimizing portfolio weights in mean-variance models.
method Functional optimization approach, treating weights as functions of past values.
result Gradient-ascent algorithms can solve functional optimization problems for mean-variance portfolio management.
New framework for optimal transport with jumps over intermediate spaces.
problem Optimal transport with mass jumps over intermediate spaces.
method Hierarchical Jump multi-marginal transport (HJMOT) on Polish spaces.
result Existence and uniqueness of Monge solutions under sequential differentiability and twist condition.
The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is further shown that the existence of a dual solution implies that the optimal tran…
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In this approach, one gets a surrogate dataset by sampling from the full data, and …
Study finds weak solutions for complex map flows with optimal lifespan.
problem Existence of weak solutions for two-phase matrix-valued harmonic map flows.
method Modified minimizing movement scheme, discretizing time and interpolating solutions.
result Existence of weak solutions with optimal lifespan for the limiting system.
Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously. However, it is often impossible to find one single solution to optimize all the tasks, since different tasks might conflict with each other. Recently, a novel method is proposed to find one single Pareto optimal solution with…
Contextual Strongly Convex Simulation Optimization: Optimize then Predict with Inexact Solutionsstat.ML
Study optimizes decisions in real-time using inexact simulation solutions.
problem Real-time decision-making in simulation optimization with inexact solutions.
method Optimize then predict (OTP) approach, analyzing bias and variance in simulation-optimization algorithms.
result Unified analysis framework for OTP, establishing convergence rates and optimal allocation of computational budget.
The main purpose of this paper is to analyze solutions to a fully nonlinear parabolic equation arising from the problem of optimal portfolio construction. We show how the problem of optimal stock to bond proportion in the management of pension fund portfolio can be formulated in terms of the solution to the Hamilton-Ja…
Improved iterative hard thresholding for faster, sparser solutions.
problem Finding sparser solutions without sacrificing runtime.
method Adaptive regularization framework applied to iterative hard thresholding.
result Returns solutions with sparsity , improving over existing methods.
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have low rank, the algorithm converges to a solution. This algorithm, SketchyCGM, modi…
Continuous Parallel Relaxation for Finding Diverse Solutions in Combinatorial Optimization Problemsstat.ML
CPRA efficiently finds diverse solutions in CO problems using UL and parallelization.
problem Finding optimal solutions often requires diverse outcomes in real-world applications.
method CPRA, an UL-based framework, discovers shared representations to generate diverse solutions.
result CPRA outperforms existing UL-based solvers in generating diverse solutions.
Bayesian method reduces misclassification errors in ranking Pareto-optimal solutions.
problem Identifying true Pareto-optimal solutions in noisy multiobjective optimization.
method Sequential allocation of extra samples using stochastic kriging to build predictive distributions.
result The proposed method outperforms existing algorithms in reducing misclassification errors.
Bayesian optimization with preference learning identifies preferred solutions in multi-objective problems.
problem Optimizing multiple criteria with decision maker preferences in expensive functions.
method Bayesian optimization with interactive preference learning and active acquisition function.
result Identifies the most preferred solution with reduced interaction cost.
Develops first closed-form portfolio formula for GARCH spot assets.
problem Optimizing portfolio allocation for assets with time-varying volatility.
method Closed-form solution for CRRA utility maximization under HN-GARCH model.
result Optimal strategy is independent of asset volatility development.
Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulatorsstat.AP
EDU method finds diverse optimal solutions for expensive simulators.
problem Optimizing expensive black-box simulators for diverse solutions.
method EDU method searches for diverse locally-optimal solutions within a tolerance level.
result EDU yields a closed-form acquisition function facilitating efficient sequential queries.
Proposes a new method to learn entire solution paths without discretization.
problem Optimizing a family of problems indexed by hyperparameters.
method Parameterizes the solution path with basis functions and solves a single stochastic optimization problem.
result Uniform error of learned path converges linearly to a constant related to basis expressiveness.
Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems subject to specific constraints, which can be formulated as variable or functional optimization. If the objective and constraint functions of a variable optimization problem can be derived, standard numerical…
A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In literature the latter is solved by assuming {\it a priori} that the problem is well-pos…
An explicit solution for an optimal stopping/optimal control problem which models an asset saleq-fin.PM
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the decision over when to sell, the agent has to choose a control strategy which corr…
Financial Portfolio Optimization: Computationally guided agents to investigate, analyse and invest!?q-fin.PM
Financial portfolio optimization is a widely studied problem in mathematics, statistics, financial and computational literature. It adheres to determining an optimal combination of weights associated with financial assets held in a portfolio. In practice, it faces challenges by virtue of varying math. formulations, par…
Survey of GANs challenges and solutions for better model design and optimization.
problem Challenges in training GANs, including mode collapse, non-convergence, and instability.
method Comprehensive survey of GANs design and optimization solutions, proposing a new taxonomy.
result Presentation of promising research directions in GANs.
Study on optimal partitions and nodal solutions for the Yamabe equation.
problem Existence and structure of optimal partitions for the Yamabe equation.
method Analysis of a weakly coupled elliptic system related to the Yamabe equation.
result Existence of least energy sign-changing solutions with precisely two nodal domains.
MOBO-OSD optimizes multi-objective functions using orthogonal search directions.
problem Challenging multi-objective optimization problem.
method Solves multiple constrained optimization problems along orthogonal search directions.
result Consistently outperforms state-of-the-art algorithms.
In this paper, we study how to solve resource allocation problems in ultra-reliable and low-latency communications by unsupervised deep learning, which often yield functional optimization problems with quality-of-service (QoS) constraints. We take a joint power and bandwidth allocation problem as an example, which mini…
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…
The present paper addresses the issue of choosing an optimal dynamic reinsurance policy, which is state-dependent, for an insurance company that operates under multiple insurance business lines. The optimal survival function is characterized as the unique nondecreasing viscosity solution of the associated Hamilton-Jaco…
FOSC-X: An extended framework for extracting multiple optimal flat clusterings from hierarchical cluster trees
problem Extracting multiple optimal flat clusterings from hierarchical cluster trees
method Dynamic programming with lower and upper feasibility bounds
result Guaranteed optimal rankings of top-M solutions with linear-time complexity
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns -approximate solutions for distributions over objectives, we compute a distrib…
Paper tackles bilevel optimization problems using penalty methods.
problem Unconstrained and constrained bilevel optimization problems with nonsmooth lower levels.
method Introduces first-order penalty methods and and operation complexities.
result Establishes operation complexities for finding -KKT solutions.
GFlowNets improve combinatorial optimization by efficiently sampling from solution spaces.
problem NP-hard combinatorial optimization problems with structured constraints.
method Design Markov decision processes and train conditional GFlowNets to sample solutions.
result GFlowNet policies find high-quality solutions efficiently on various CO tasks.
In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We present a MIO approach for solving the classical best subset selection problem o…
BILBO optimizes bilevel problems without repeated lower-level optimizations.
problem Challenges in bilevel optimization, especially in noisy, constrained, and derivative-free settings.
method BILevel Bayesian Optimization (BILBO) that optimizes both levels simultaneously, using confidence-bounds and function query selection.
result Theoretical and empirical evidence of BILBO's effectiveness on various problems.
On compact manifolds which are not simply connected, we prove the existence of "fake" solutions to the optimal transportion problem. These maps preserve volume and arise as the exponential of a closed 1 form, hence appear geometrically like optimal transport maps. The set of such solutions forms a manifold with dimensi…
We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements from a given system of elements. There is an increasing interest in building such …
A popular approach of achieving fairness in optimization problems is by constraining the solution space to "fair" solutions, which unfortunately typically reduces solution quality. In practice, the ultimate goal is often an aggregate of sub-goals without a unique or best way of combining them or which is otherwise only…
Algorithm ensures privacy while strictly adhering to constraints.
problem Differential privacy with linear constraints that must be strictly followed.
method Developed an algorithm that releases a nearly-optimal solution satisfying constraints with probability 1.
result Achieved nearly optimal performance while preserving privacy and strictly adhering to constraints.
BP fails to find sparsest solution for structured matrices.
problem Finding sparsest solution to linear equations with structured matrices.
method Introduced class of structured matrices for BP failure.
result Determines columns corresponding to unrecoverable non-zero entries.
New algorithm reduces robust optimization scale for better constraint satisfaction.
problem Finding robust solutions to optimization problems with unknown constraints.
method Empirical domain reduction to determine robustness scale.
result Our algorithm's scale is less affected by parameter dimensionality.
Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of Neyman-Pearson type binary solution. We add a constraint on expected return to investigate the Mean-CVaR portfolio sele…
Modified K-means ensures local optimality with same complexity.
problem Lack of rigorous analysis on local optimality guarantees of K-means.
method Proposed modifications to K-means ensuring local optimality.
result Proposed methods provide improved locally optimal solutions.
Real-world problems typically require the simultaneous optimization of several, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions, which further increases the complexity of optimization. …
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under some assumptions on the underlying process and the utility function. The resultin…
This work proposes an unsupervised neural network framework for solving combinatorial optimization problems on graphs.
problem Challenges in neural networks solving combinatorial optimization problems without labeled instances.
method Inspired by Erdos' probabilistic method, a neural network parametrizes a probability distribution over sets, optimizing it to find low-cost integral solutions.
result The method provides valid solutions to the maximum clique problem and local graph clustering, achieving competitive results.