Work establishes conditions for bias-free policy optimization.
problem Improving policy optimization methods without introducing bias.
method Established conditions for parametric critic without bias.
result Identified bias in current policy optimization algorithms.
Large deviations theory applied to policy gradient methods.
problem Understanding convergence of policy gradient methods in reinforcement learning.
method Large deviation rate function and contraction principle from large deviations theory.
result Convergence properties of policy gradient methods can be extended to various policy parametrizations.
Optimizes fairness without sacrificing primary objectives.
problem Achieving fairness in optimization without reducing solution quality.
method Parametrized objective function to generate a set of optimal solutions, then optimize fairness using secondary criteria.
result Optimal solutions can be found that balance fairness and primary objectives.
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, …
Parametric t-SNE improves generalization for streaming data.
problem Training neural networks for t-SNE objective function fails due to gradient exploding.
method Applied gradient clipping to solve gradient exploding problem.
result Parametric t-SNE achieves quality compatible with non-parametric t-SNE while generalizing to new data.
Method designs lightweight, structurally robust shell objects.
problem Designing lightweight, structurally robust shell objects under external forces.
method Shape parametrization based on Laplace's equation for smooth, intersection-free boundaries; gradient-free optimization algorithm.
result Practical solution to structural design of hollow objects with single inner cavity.
Together with the Moebius strip, the Klein bottle is one of the intriguing objects in the universe of geometry, sometimes appearing in non-mathematical contexts too. Until now, several parametrizations of it as a surface immersed in ordinary three-space have been found, some of which are very elegant and lead to nice a…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the present paper is to provide a short overview of some results and open problems on s…
Parametric insurance offers better risk-sharing in high-risk settings than traditional indemnity insurance.
problem High-risk environments where traditional indemnity insurance is unaffordable or ineffective.
method Comparison of excess-of-loss indemnity insurance and parametric insurance within a mean-variance framework, considering fixed costs and binding budget constraints.
result Parametric insurance yields higher welfare for risk-averse individuals, especially when indemnity insurance is impractical.
Calculating similarities between objects defined by many heterogeneous data modalities is an important challenge in many multimedia applications. We use a multi-modal topic model as a basis for defining such a similarity between objects. We propose to compare the resulting similarities from different model realizations…
In recent work on both generative and discriminative score to log-likelihood-ratio calibration, it was shown that linear transforms give good accuracy only for a limited range of operating points. Moreover, these methods required tailoring of the calibration training objective functions in order to target the desired r…
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the transformation group principle (smooth geometric objects and their discretizations are invar…
Informative Bayesian priors are often difficult to elicit, and when this is the case, modelers usually turn to noninformative or objective priors. However, objective priors such as the Jeffreys and reference priors are not tractable to derive for many models of interest. We address this issue by proposing techniques fo…
Local-HDP learns independent topics for each 3D object category in real-time.
problem Learning independent topics for each 3D object category in real-time.
method Local-Hierarchical Dirichlet Process (Local-HDP) with online variational inference.
result Local-HDP outperforms other approaches in accuracy, scalability, and memory efficiency.
Proposes a novel algorithm for multi-objective reinforcement learning.
problem Challenges in setting numerical preferences for objectives in different units and scales.
method Learn action distributions for each objective and use supervised learning to fit a parametric policy.
result Demonstrates effectiveness on robotics tasks, allowing tracing out the space of nondominated solutions.
Highly Autonomous Driving (HAD) systems rely on deep neural networks for the visual perception of the driving environment. Such networks are trained on large manually annotated databases. In this work, a semi-parametric approach to one-shot learning is proposed, with the aim of bypassing the manual annotation step requ…
Simple greedy algorithms can excel in multi-objective bandits with multiple good arms.
problem Optimizing multiple objectives in bandits is traditionally harder.
method Introduced greedy algorithms that exploit multiple good arms for multiple objectives.
result Simple greedy algorithms achieve strong performance in multi-objective bandits.
Tests for equivariance in non-parametric regression models.
problem Detecting false assumptions of symmetry in regression models.
method Develops tests for G-equivariance independent of the model. result Confidence in using equivariant models when symmetry is unknown.
Minimal surfaces with planar curvature lines are classical geometric objects, having been studied since the late 19th century. In this paper, we revisit the subject from a different point of view. After calculating their metric functions using an analytical method, we recover the Weierstrass data, and give clean parame…
A new algorithm difFOCI improves feature learning from data.
problem Feature selection and learning from data.
method Parametric, differentiable approximation of FOCI method.
result Improves feature learning with better management of spurious correlations.
New method optimizes multiple objectives in A/B testing for AI and clinical trials.
problem Minimizing cumulative regret, maximizing CATE, and ensuring differential privacy in large-scale experiments.
method ConSE and DP-ConSE algorithms for sequential segmentation and elimination, achieving Pareto-optimal frontier.
result Privacy comes 'for free' in our framework, with only asymptotically negligible costs to regret and accuracy.
Estimates non-parametric logistic model using case-control data and external summary info.
problem Imbalanced binary data in case-control studies.
method Two-step estimation procedure with deep neural network for functional approximation.
result Proposed estimator achieves optimal convergence rate in non-parametric regression.
Proposes a parametric modal regression method using the implicit function theorem.
problem Finding conditional modes for multi-modal conditional distributions.
method Uses the implicit function theorem to develop an objective function for learning a joint function over inputs and targets.
result Empirically demonstrates scalability and effectiveness in learning multi-valued functions and high-dimensional inputs.
The paper develops efficient estimators for semi-parametric binary models in distributed computing.
problem Estimation and inference challenges in large-scale data under non-smooth objective functions.
method Proposes one-shot and multi-round divide-and-conquer estimators with adaptive kernel smoothing to relax constraints and achieve superlinear optimization error.
result Establishes quadratic convergence up to optimal statistical error rate and handles dataset heterogeneity and high-dimensional sparse parameters.
Bayesian approach improves uncertainty in deep learning models.
problem Uncertainty quantification in deep learning models.
method Bayesian point of view, Gaussian approximability, semi-parametric Bernstein-von Mises theorems.
result Bayesian credible regions have valid frequentist coverage, providing theoretical justification for deep learning.
New MCFOs improve learning generative models and time series inference.
problem Challenges in learning generative models and inferring latent trajectories for time series.
method Proposed Monte Carlo filtering objectives (MCFOs) for joint learning and adaptive proposals.
result MCFOs lead to efficient and stable model learning and explain data well.
Develops neural network framework for risk-reward optimization problems.
problem Multi-period risk-reward optimization with constrained policies.
method Neural network framework with two coupled feedforward networks, parametrizing two-step policies.
result Empirical optimum converges to true optimal value as network capacity and training size increase.
New method smooths optimization for sparse regularization.
problem Non-smooth, non-convex optimization problems for sparsity.
method Overparameterization and smooth surrogate penalties.
result Surrogate objective has identical global and local minima.
Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) appr…
New method distinguishes cause from effect using causal velocity.
problem Inferring causal direction from bivariate data.
method Parametrization of bivariate SCMs in terms of causal velocity, using tools from measure transport.
result Method extends beyond known model classes and requires no assumptions on noise distributions.
Improved complexity for machine learning optimization methods.
problem Optimizing over-parametrized models in machine learning.
method Stochastic conditional gradient methods with interpolation-like conditions.
result Improved oracle complexities for finding optimal solutions.
In many real life problems, objects are described by large number of binary features. For instance, documents are characterized by presence or absence of certain keywords; cancer patients are characterized by presence or absence of certain mutations etc. In such cases, grouping together similar objects/profiles based o…
A new algorithm improves efficiency and robustness of heuristic optimization in simulation-based problems.
problem Optimizing input parameters for stochastic simulation-based optimization.
method Reactive sample size algorithm based on parametric tests and indifference-zone selection.
result The reactive method improves efficiency and robustness of heuristic optimization techniques.
New function class characterizes loss landscape of deep neural networks without over-parametrization.
problem Complex loss landscape of deep neural networks without over-parametrization.
method Proposed a novel class of functions to characterize loss landscape without over-parametrization.
result Gradient-based optimizers possess theoretical guarantees of convergence under the new function class assumption.
New limits of minimal surface systems have surprising large interior parts.
problem Minimal surface system limits with large interior vertical and non-minimal portions.
method Construction of limits with smallest possible dimension and codimension.
result Limits of minimal surface systems can have surprising large interior parts.
New unbiased gradient estimators for complex optimization problems.
problem Unbiased and variance-limited gradient estimation for conditional stochastic optimization.
method Developed multilevel Monte Carlo gradient estimators for conditional stochastic optimization problems.
result Unbiased and finite variance gradient estimators for conditional stochastic optimization problems.
Descending phase retrieval algorithms show a phase transition with increasing sample complexity.
problem Theoretical limits of descending phase retrieval algorithms.
method Utilizing Random duality theory (RDT), the study develops a generic program to characterize algorithm performance.
result As sample complexity increases, the parametric manifold transitions from multi to single funneling points, leading to a phase transition in algorithm success.
Unified framework for nonconvex matrix completion with linearly parameterized factors.
problem Matrix completion with improved accuracy using linearly parameterized factors.
method Unified nonconvex optimization framework with Correlated Parametric Factorization condition.
result Uniform upper bounds for low-rank estimation at any local minimum.
Optimistic actor-critic tackles linear MDPs with parametric policies.
problem Theoretical limitations of existing actor-critic methods for linear MDPs.
method Proposes an optimistic actor-critic framework with parametric log-linear policies and approximate Thompson sampling.
result Achieves state-of-the-art sample complexity in both on-policy and off-policy settings.
A tractable pseudo-metric for non-parametric distributions via SPD geometry.
problem Computing distances between non-parametric probability distributions is intractable.
method Two-stage framework: projection onto parametric family, embedding into SPD matrices.
result Closed-form pseudo-metric for two-sample hypothesis testing.
Method estimates forces from agent trajectories to infer static obstacles.
problem Estimating forces from agent trajectories to infer static obstacles.
method Artificial neural networks to estimate non-parametric velocity fields.
result Incrementally learns velocity fields due to static objects.
Non-parametric approaches for analyzing network data based on exchangeable graph models (ExGM) have recently gained interest. The key object that defines an ExGM is often referred to as a graphon. This non-parametric perspective on network modeling poses challenging questions on how to make inference on the graphon und…
This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GANs), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonpar…
Efficiently optimizes orthogonal and Stiefel matrices on parallel units.
problem Optimization over orthogonal groups on parallel units.
method CWY and T-CWY transforms for parametrization and optimization.
result CWY and T-CWY methods lead to convergence on parallel units.
EGL optimizes complex functions without fitting them, achieving state-of-the-art results.
problem Optimizing high-dimensional, non-convex functions in AI tasks.
method EGL trains a neural network to estimate the objective gradient directly, not fitting the function.
result EGL achieves state-of-the-art results in challenging optimization problems.
Paper proposes a policy-search algorithm to learn entropy-maximizing exploration policies in reward-free environments.
problem Reward-free learning in high-dimensional, continuous-control domains.
method Maximum Entropy POLicy optimization (MEPOL) algorithm that maximizes a non-parametric state entropy estimate.
result MEPOL learns a maximum-entropy exploration policy that facilitates learning various reward-based tasks.
Two methods for pricing swing contracts using neural networks or explicit functions.
problem Evaluating optimal energy purchases in swing contracts with firm constraints.
method Two approaches: explicit parametric function and neural network approximation.
result Neural network approach provides better prices in shorter computation time.
In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses which is invariant to the functional form of the transformation function. We prove t…