A new algorithm approximates optimal stopping problems with semi-tractable complexity.
problem Approximating the value of optimal stopping problems in discrete and continuous time.
method Weighted Stochastic Mesh (WSM) Algorithm for discrete and continuous time optimal stopping problems.
result WSM leads to semi-tractable complexity in discrete cases, with complexity bounded by ε − 4 log d + 2 ( 1 / ε ) \varepsilon^{-4}\log^{d+2}(1/\varepsilon) ε − 4 log d + 2 ( 1/ ε ) . We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from and the target distribution is log-concave, this can be tractably solved with c…
New algorithm achieves optimal regret in average reward MDPs without prior bias information.
problem Achieving optimal regret in average reward MDPs with computational efficiency and without prior bias information.
method Projective Mitigated Extended Value Iteration (PMEVI) to compute bias-constrained optimal policies efficiently.
result First tractable algorithm with minimax optimal regret of O ~ ( s p ( h ∗ ) S A T ) \widetilde{\mathrm{O}}(\sqrt{\mathrm{sp}(h^*) S A T}) O ( sp ( h ∗ ) S A T ) . Optimizes ICA performance in high dimensions with computational constraints.
problem Statistical optimality and computational tractability in ICA.
method Characterization of optimal sample complexity, development of computationally tractable estimates.
result Optimal sample complexity is linear in dimensionality, quadratic with low-degree polynomial algorithms.
Study shows tractable generalization in RL is impossible but possible with Strong Proximity.
problem RL agents struggle to generalize to new environments.
method Introduced Weak and Strong Proximity conditions to capture similarity between environments.
result Proved Strong Proximity is sufficient for efficient generalization.
Fixed-parameter tractability of private synthetic data generation
problem Generating synthetic data under differential privacy
method Linear programming and subsampled private multiplicative weights method
result Optimal error rates across all regimes
New method models Poisson intensity using RKHS for high-dimensional data.
problem Tractable nonparametric modeling of inhomogeneous Poisson intensity functions.
method Reproducing Kernel Hilbert Space (RKHS) formulation for intensity functions.
result Optimization of penalized likelihood can be cast as a tractable finite-dimensional problem.
Paper shows how to infer hidden states in neural networks analytically.
problem Intractability of Bayesian inference for neural networks.
method Leverage tractable approximate Gaussian inference (TAGI) for hidden states inference.
result Demonstrates inference of hidden states through constraints for various applications.
Survey of tractable nonconvex problems using symmetry.
problem Nonlinear models with symmetries create complex, nonconvex objective landscapes.
method Analysis of geometric structure and symmetry roles.
result Efficient methods can find global minimizers due to symmetry.
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal encoding/decoding strategies, which are of significant relevance to Computational Neuroscien…
Optimizes liquidity provision intervals for profitable AMM participation.
problem Financial losses from poor liquidity provision intervals and reallocation costs.
method Developed a tractable stochastic optimization problem.
result Computes optimal liquidity provision intervals for profitable liquidity concentration.
Bayesian model captures spatial correlations in data.
problem Modeling spatial correlations in high-dimensional data.
method Structured Bayesian Gaussian process latent variable model with parameterized spatial kernel and structure-exploiting algebra.
result Inference is tractable with computational complexity similar to traditional Bayesian GP-LVM.
New lower bounds improve logistic log-likelihood optimization and inference.
problem Designing computationally tractable lower bounds for logistic log-likelihoods.
method Developed a piece-wise quadratic lower bound that uniformly improves tangent quadratic minorizers.
result Improves the speed of convergence and accuracy of variational Bayes approximations.
Two new methods for variational inference without tractable densities.
problem Challenges in variational inference due to computationally intractable probability density functions.
method Introduces wild variational inference methods that do not require tractable density functions.
result Significant improvement in stochastic gradient Langevin dynamics (SGLD) step size adjustment.
New approach optimizes dynamic decisions with side info.
problem Optimizing decisions under uncertainty with additional data.
method Combines machine learning with robust optimization.
result Proves asymptotic optimality and achieves significant improvements.
In intractable, undirected graphical models, an intuitive way of creating structured mean field approximations is to select an acyclic tractable subgraph. We show that the hardness of computing the objective function and gradient of the mean field objective qualitatively depends on a simple graph property. If the tract…
The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true likelihood. But due to requirement for model-specific derivation of the optimization equa…
BO method improved by density-ratio estimation for better efficiency and scalability.
problem Limitations in Bayesian optimization due to analytical tractability of predictive models.
method Reformulated Bayesian optimization by casting expected improvement as a binary classification problem.
result Improved efficiency and scalability of Bayesian optimization.
The paper develops sum-of-squares relaxations for computing f f f -divergences.
problem Computing f f f -divergences from non-centered covariance matrices. method Sum-of-squares relaxations for convex optimization.
result Sum-of-squares relaxations make computations tractable.
This work tackles slate-based recommender systems using RL, optimizing long-term user engagement.
problem Optimizing long-term user engagement in slate-based recommender systems.
method Developed SLATEQ, a decomposition of RL methods for slate-based recommendations, and outlined a practical methodology.
result SLATEQ decomposes long-term value of a slate into component item-wise long-term values under mild assumptions.
We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.
problem Matching objects between incomparable spaces using the Gromov-Wasserstein distance.
method Semi-definite programming (SDP) relaxation of the GW distance.
result The SDP relaxation provides globally optimal solutions for the GW distance in some instances.
Boosting variational inference uses optimization to improve posterior approximations.
problem Improving the tractability of Bayesian posterior approximations.
method An optimization-based approach to greedily add components to a mixture of densities.
result Established convergence properties and rates for the boosting variational inference algorithm.
We introduce RNADE, a new model for joint density estimation of real-valued vectors. Our model calculates the density of a datapoint as the product of one-dimensional conditionals modeled using mixture density networks with shared parameters. RNADE learns a distributed representation of the data, while having a tractab…
We develop computationally efficient Riemannian manifolds for graph embeddings.
problem Challenging to maintain computational tractability in non-Euclidean graph embeddings.
method Explore computationally efficient matrix manifolds for graph embeddings.
result Consistent improvements over Euclidean geometry and outperforming hyperbolic and elliptical embeddings.
New method for predicting portfolio dynamics using non-Euclidean geometry.
problem Predicting efficient portfolios with geometric structure.
method Non-Euclidean conditional expectation and filtering equations.
result Accurate numerical forecasts of portfolio dynamics.
New algorithms compute robustness bounds for multiclass classification models.
problem Computing robustness of deep learning models in multiclass classification.
method Optimal transport and linear programming/entropic regularization.
result Tractable algorithms for computing robustness bounds.
Optimizes bank capital structure under Basel III constraints, simplifying complex dynamics.
problem Optimizing risky investments, dividends, and capital structure under Basel III constraints.
method Formulated as a stochastic control problem, reducing dynamics to a one-dimensional process in leverage ratio.
result Simple policy: pay dividends at an upper barrier and recapitalize at the distress boundary.
Considering mean-variance portfolio problems with uncertain model parameters, we contrast the classical absolute robust optimization approach with the relative robust approach based on a maximum regret function. Although the latter problems are NP-hard in general, we show that tractable inner and outer approximations e…
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.
We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models and Delta's method (estimating functions of linear regression models) as well. …
Unified framework for tractable inference scenarios in machine learning models.
problem Complex inference scenarios in machine learning models.
method Characterization of tractable modular operations over circuits and derivation of a unified framework.
result Unified framework for reasoning about tractable models.
New methods optimize sums of bivariate functions on finite domains.
problem Optimizing functions with multiple arguments that are sums of bivariate functions.
method Measure-valued extensions, ℓ 2 \ell^2 ℓ 2 -approximation, entropy-regularization, linear programming, coordinate ascent. result Tractable problem formulations solvable with various methods.
New approach to convex hulls for low-rank problems.
problem Characterizing convex hulls for low-rank sets.
method Matrix perspective function and orthogonal projection matrices.
result Strong relaxations for various low-rank problems.
New algorithms improve robust estimation in contaminated Gaussian models.
problem Simultaneous estimation of location and variance matrix in contaminated Gaussian models.
method Tractable adversarial algorithms with spline discriminators for robust estimation.
result Achieve minimax optimal rates or near-optimal rates under Huber's contamination model.
Improves scalability of Bayesian optimization for combinatorial spaces.
problem Optimizing expensive functions over large combinatorial spaces.
method Parametrized Submodular Relaxation (PSR) to solve AFO problems for BOCS.
result Significant improvements in scalability and accuracy for BOCS model.
Autoencoder optimizes data embedding for accurate PDF reproduction.
problem Inaccurate PDF reproduction in latent space of VAEs.
method Rate-Distortion Optimization guided autoencoder with isometric property.
result Our method achieves isometric data embedding and tractable PDF relations.
New framework solves low-rank optimization problems to certifiable optimality.
problem Low-rank optimization problems with certifiable solutions.
method Mixed-Projection Conic Optimization framework using symmetric projection matrices and outer-approximation algorithms.
result Solves low-rank problems to certifiable optimality, outperforming existing methods.
OMLE combines optimism and MLE for efficient sequential decision making.
problem Efficiently solving sequential decision making problems, especially in partially observable settings.
method Combines optimism for exploration and maximum likelihood estimation for model learning.
result OMLE learns near-optimal policies for a wide range of sequential decision making problems.
Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with nonparametric models, the optimal solution is harder to compute. Current approach…
Kernel semi-implicit variational inference improves variational inference without additional optimization.
problem Intractability of hierarchical semi-implicit distributions in variational inference.
method Kernel semi-implicit variational inference (KSIVI) using kernel methods to eliminate lower-level optimization.
result KSIVI reduces variational inference to kernel Stein discrepancy (KSD) optimization, improving expressiveness and tractability.
New framework for conditional risk minimization using optimal transport.
problem High-stakes decisions with side information, especially economic conditions.
method Universal framework based on union-ball formulation in optimal transport.
result Offers interpretability, tractability, and scalability for various risk functionals.
New model incorporates long-range dependence in mortality rates for better valuation and risk management.
problem Lack of appropriate models for valuing and managing mortality securities with long-range dependence.
method Proposes a novel class of Volterra mortality models that incorporate LRD, derived in closed-form solution.
result Models provide flexibility and tractability for valuing and hedging mortality-related products.
Optimistic RL algorithms are simplified for deep RL with competitive performance.
problem Achieving accurate optimism in model-based RL for large-scale problems.
method Interpreting scalable optimistic model-based algorithms as solving a tractable noise augmented MDP.
result Competitive regret bound of i l d e O ( ∣ S ∣ H ∣ A ∣ T ) ilde{\mathcal{O}}( |\mathcal{S}|H\sqrt{|\mathcal{A}| T } ) i l d e O ( ∣ S ∣ H ∣ A ∣ T ) for Gaussian noise augmentation. PNCs balance tractability and expressiveness in probabilistic modeling.
problem Balancing tractability and expressiveness in probabilistic models.
method Introduce probabilistic neural circuits (PNCs) as a mix of Bayesian networks and neural networks.
result PNCs are powerful function approximators.
New algorithm tackles multimodal bandits with optimal regret bounds.
problem Stochastic multi-armed bandit problem with multimodal rewards.
method Proposed computationally tractable algorithm for multimodal rewards.
result Asymptotically optimal algorithms implemented for the bandit problem.
This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using tools from stochastic control, and how to rigorously verify their optimality by mea…
The paper tackles voltage control in distribution systems with uncertainties using chance constraints.
problem Voltage control in distribution systems with high uncertainties from distributed energy resources.
method Chance constraint approach accounting for arbitrary correlations, solved via stochastic quasi gradient method.
result The method is more robust and computationally tractable compared to conventional approaches.
Study optimal execution in a transient price impact model with multiple traders.
problem Optimal execution among multiple traders with transient price impact.
method Analyzed N N N -player optimal execution games in an Obizhaeva--Wang model with and without regularization. Derived equilibrium solutions and explained their behavior. result Existence of equilibrium restored with a specific time-dependent cost on block trades, and equilibrium is tractable.