Estimating IPM is as hard as estimating under IPM, both requiring similar optimal rates.
problem Estimating Integral Probability Metrics (IPMs) between probability measures.
method Study of minimax optimal rates for IPM estimation and under IPM estimation based on samples.
result Minimax optimal rates for estimating IPM and estimating under IPM are multiplicatively equivalent.
Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.
problem Adapting optimal transport for ε-contaminated sets. method Generalized optimal transport problems with lower probabilities, showing equivalence under ε-contaminations. result Monge's and Kantorovich's problems coincide under ε-contaminated sets, but not always. Optimizes risk-neutral probabilities for derivative pricing.
problem Deriving bounds on derivative values under multiple risk-neutral scenarios.
method Convex optimization over the set of risk-neutral probability distributions.
result Tractable finite-dimensional optimization problems for pricing.
Study shows optimal rates for estimating Wasserstein metric and measures.
problem Minimax optimal estimation of Wasserstein metric between probability measures.
method Analyzes the minimax rates for estimating the Wasserstein-1 metric and probability measures.
result Minimax optimal rates for estimating Wasserstein metric and measures are multiplicatively equivalent.
Optimizes insurance pricing to minimize ruin probability under various claim dependencies.
problem Determining optimal insurance premiums in the presence of dependencies between claim occurrences.
method Analyzes both independent and dependent claim processes, considering single and multiple risks.
result Optimal insurance premiums depend on initial reserve and claim dependencies.
New algorithms achieve high probability second-order convergence in non-convex optimization.
problem Stochastic non-convex optimization with high probability second-order convergence.
method Proposed NCG-S updating step and two algorithms.
result First algorithms with high probability second-order convergence and almost linear time complexity.
This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.
problem Optimizing functions of probability measures with displacement convex properties.
method Particle gradient descent applied to displacement convex functions with theoretical guarantees.
result Finite number of particles and computations are sufficient to find optimal solutions for displacement convex functions.
Robust portfolio optimization considers uncertainty in market probabilities.
problem Uncertainty in market probabilities in multiperiod portfolio selection.
method Robust mean-variance optimization using Wasserstein ball centered at empirical data.
result Numerical simulations show improved performance compared to other strategies.
Optimal transport learns Riemannian metrics for evolving probability measures.
problem Learning metrics for evolving probability measures on Riemannian manifolds.
method Neural parametrization of a metric tensor via optimal transport, alternating optimization scheme.
result Improved trajectory inference on scRNA and bird migration data.
Proposes qPO, a new acquisition strategy for batched Bayesian optimization that maximizes the probability of including the optimum.
problem Efficiently identifying top-performing compounds from a large chemical library.
method qPO (multipoint Probability of Optimality) acquisition strategy that maximizes the probability of including the true optimum.
result Empirical evidence shows that qPO is competitive with and complements other state-of-the-art methods in batched Bayesian optimization.
A new kernel for probability measures based on optimal transport.
problem Efficiently comparing and modeling distributions.
method Kernel over probability measures using regularized optimal transport and Hilbertian embedding.
result The proposed kernel enables Gaussian process modeling on distributions with theoretical and computational advantages.
The paper accelerates gradient flows on probability distributions using optimal control theory.
problem Optimizing probability distributions efficiently.
method Variational formulation and Hamilton's equations for accelerated gradient flows.
result The method achieves accelerated density transport from any initial distribution to a target distribution.
Optimal insurance minimizes ruin probability with non-decreasing functions.
problem Minimizing ruin probability with insurance premiums and non-decreasing functions.
method Reformulated problem with inverse survival function as control variable.
result Deductible insurance with maximum limit is optimal.
NNLMs optimize poorly for word probabilities due to embedding space structure.
problem NNLMs assign suboptimal probabilities to some words.
method Analyzed the inductive bias of NNLMs and the structure of word embeddings.
result Words on the convex hull have bounded probability, affecting others.
Maximizes probability of completing investment schedules with optimal portfolio weights.
problem Optimizing probability of completing investment schedules with optimal portfolio weights.
method Computing maximum probability and optimal portfolio weight functions for various rebalancing schedules.
result Noticeable improvements in probability to complete schedules with optimal portfolio weights.
Optimizes reinsurance and investment strategies to minimize ruin probability.
problem Optimizing reinsurance and investment strategies to minimize ruin probability.
method Stochastic projected gradient method based on Malliavin calculus.
result Effectiveness of the proposed method demonstrated through numerical experiments.
Two BO methods improve reliability optimization for rare failures.
problem Maximizing reliability of designs subject to random perturbations.
method Bayesian optimization with Thompson sampling and knowledge gradient.
result Proposed methods outperform existing techniques in extreme failure probability scenarios.
Paper improves tree probability estimation using stochastic optimization and variance reduction.
problem Improving tree probability estimation in phylogenetic inference.
method Introduces computationally efficient methods for training SBNs and variance reduction for optimization.
result Methods outperform previous baseline methods in tree topology probability estimation and Bayesian phylogenetic inference.
New algorithms estimate and test collision probability with near-optimal sample complexity.
problem Estimating and testing collision probability in discrete distributions.
method Developed algorithms for (α,β)-local differential privacy and sequential testing. result Achieved nearly optimal sample complexity for estimating and testing collision probability.
The paper integrates behavioral distortions into portfolio optimization using implied probability weighting functions.
problem Behavioral distortions in probability weighting affect portfolio optimization under different return distributions.
method Developed a unified framework to extract probability weighting functions from optimal portfolios modeled under Gaussian and NIG distributions.
result Increasing tail fatness amplifies behavioral distortions, and shifts in risk-free rates alter the curvature of these distortions.
Study generalizes property elicitation to imprecise probabilities.
problem Minimizing risk over imprecise probability distributions.
method Maximin risk minimization over a set of imprecise probabilities.
result Conditions for elicitability of IP-properties.
Paper derives necessary optimality condition for portfolio selection with distorted probabilities.
problem Continuous-time portfolio selection with S-shaped utility and probability distortions.
method Derives necessary condition for optimality using cumulative prospective theory.
result Derives a necessary condition for optimality in a behavioral portfolio selection problem.
New averaging strategy achieves optimal convergence rate with high probability.
problem Optimizing convergence rate for strongly-convex functions.
method Simple non-uniform averaging strategy combined with Freedman's inequality.
result Achieves optimal O(1/T) convergence rate with high probability. Study on optimal rates for sequential probability assignment using smoothed analysis.
problem Optimal rates for sequential probability assignment under smoothed adversaries.
method General-purpose reduction from minimax rates to transductive learning, development of an efficient algorithm using MLE oracle.
result Optimal (logarithmic) fast rates for parametric and finite VC dimension classes, sublinear regret for general classes.
Proposes efficient subsampling for logistic regression with optimal probabilities.
problem Efficiently approximating maximum likelihood estimate in logistic regression for large datasets.
method Develops subsampling algorithms for logistic regression, derives optimal subsampling probabilities, and proposes two-step approximation.
result Optimal subsampling reduces computing time significantly while maintaining estimator consistency and normality.
VI approximates complex densities faster than classical methods.
problem Approximating complex probability densities.
method Optimization of a family of probability density functions using KL divergence.
result VI converges faster than Markov Chain Monte Carlo.
Study linearizes 2-Wasserstein space using optimal transport maps.
problem Stability and linearization of the 2-Wasserstein space.
method Explicit embedding of probability measures into a Hilbert space using optimal transport maps.
result The embedding is (bi-)Hölder continuous, with stability results for optimal transport maps.
The paper analyzes how contagion affects the survival probability of investment groups in microfinance.
problem The impact of contagion on the survival probability of investment groups in microfinance.
method A probabilistic approach to compute group survival probability with and without contagion effects.
result In homogeneous groups, including more members increases the probability of eventual default to 1.
Optimizes functionals on probability space using ICNNs.
problem Optimizing functionals on the space of probabilities with high-dimensional convex functions.
method Proposes an approach using input-convex neural networks (ICNNs) to approximate the JKO scheme.
result Demonstrates feasibility and validity in approximating solutions of PDEs and molecular discovery.
Optimal testing of discrete distributions with high probability, achieving sample complexity bounds.
problem Testing discrete distributions with high probability accuracy.
method Characterizing sample complexity as a function of parameters like δ, providing sample-optimal testers.
result Optimal algorithms for closeness and independence testing, achieving within constant factors of information-theoretic lower bounds.
Method solves complex optimization problems with high probability bounds.
problem Nonlinear equality constrained stochastic optimization problems.
method Step-search sequential quadratic programming method.
result High-probability bound on iteration complexity for first-order stationarity.
We interpret policy optimization as Wasserstein gradient flows and develop efficient algorithms.
problem Unclear mathematical principle of policy optimization in reinforcement learning.
method Interpreting policy optimization as Wasserstein gradient flows, developing efficient algorithms to solve the corresponding discrete gradient flows.
result Policy optimization becomes a convex problem in terms of distribution optimization under specified circumstances.
Two insurance companies collaborate to maximize the probability of none going bankrupt.
problem Maximizing the probability of no company bankruptcy in a correlated Brownian motion model.
method Analyzing optimal strategies and deriving explicit formulas for minimal ruin probability.
result Maximizing collaboration benefits when Brownian motions are positively correlated.
CREDO assesses decision optimality under uncertainty without assuming a model.
problem Uncertainty in decision-making without reliable quantification of optimality.
method CREDO uses the inverse feasible region and conformal prediction balls to estimate decision optimality probability.
result CREDO provides accurate, efficient, and reliable evaluations of decision optimality.
Efficiently approximates softmax probabilities for large-scale inference.
problem High cost of computing softmax probabilities for large-scale inference.
method Introduces a lower bound on softmax probabilities as a product of pairwise probabilities, scalable through stochastic optimization and subsampling.
result Demonstrates that the new bound has interesting theoretical properties and can be used in classification problems.
The paper solves portfolio optimization problems with risk constraints.
problem Maximizing utility while ensuring a certain wealth threshold with risk constraints.
method Derives Nash equilibria for two agents and characterizes them for more than two agents.
result Characterizes Nash equilibria for different cases of competition probabilities.
This paper calculates the exact probability distribution of hypervolume improvement for bi-objective problems.
problem Calculating the exact probability distribution of hypervolume improvement in bi-objective problems.
method Cell partition-based method to derive the probability distribution of hypervolume improvement from a bi-variate Gaussian random variable.
result The proposed ε-PoHVI acquisition function outperforms other related functions in Bayesian optimization. A new method for averaging probability distributions based on optimal weak mass transport.
problem Averaging probability distributions in a geometric way.
method Weak barycenters based on optimal weak mass transport.
result Extracts common geometric information shared by all input distributions.
Two new couplings for probability distributions are constructed and analyzed.
problem Constructing optimal couplings for two probability distributions.
method Optimizes constrained Monge-Kantorovich transport problems with supermartingales.
result Two new couplings are identified and characterized.
The study optimizes distribution estimation from samples with relative entropy error, adapting to sparse distributions.
problem Estimating discrete distributions with high-probability accuracy in relative entropy.
method Analysis of Laplace estimator and confidence-dependent smoothing techniques, including data-dependent smoothing.
result Optimal high-probability risk bounds for various estimators, including a new data-dependent smoothing method.
We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally c…
The paper defines projections for Wasserstein distances to preserve convex order in probability measures.
problem Designing sampling techniques to preserve convex order in probability measures.
method Defining projections for Wasserstein distances and solving optimization problems.
result The projections do not depend on ρ in dimension 1 and their quantile functions are explicit.
New strategy optimally identifies best arm in unknown variance Gaussian bandits.
problem Identifying the best arm in two-armed Gaussian bandits with unknown variances.
method Proposes a Neyman Allocation (NA)-Augmented Inverse Probability weighting (AIPW) strategy to estimate variances and draw arms adaptively.
result Demonstrates asymptotic optimality of the proposed strategy in the small-gap regime.
Optimizes dividend payments for insurance companies under uncertain drift.
problem Valuation and optimal dividend strategy for insurance companies with partial information.
method Bayesian approach, filter derivation, Hamilton-Jacobi-Bellman equation, numerical approximation.
result Optimal dividend strategy and value function derived for complete information.
Develops a gradient flow for Muon optimizer, a method for optimization.
problem Optimization of complex systems with matrix-valued parameters.
method Gradient flow on probability measures induced by regularized Muon optimizer.
result Derives continuous-time limits and proves Hamiltonian dissipation.
Paper compares neural network approaches to Optimal Transport.
problem Learning Optimal Maps between probability distributions.
method Two categories of approaches: heuristic and math-justified. Novel approach involves dynamic flows and supervised learning.
result Novel approach involving dynamic flows and reductions of Optimal Transport to supervised learning.
We propose and analyze a new parallel coordinate descent method---`NSync---in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen non-uniformly. We derive convergence rates under a strong convexity assumption, and comment on how to assign probabilities t…
New method speeds up optimization over probability measures.
problem High computational overhead in optimizing probability measures.
method Randomized coordinate descent on Wasserstein space.
result Significant speedups over full-gradient methods.