Proposes data-driven methods for estimating conditional expectations.
problem Estimating conditional expectations when underlying density is unknown.
method Data-driven techniques to directly estimate conditional expectations from training data.
result Extends data-driven method to solve nonlinear equations in stochastic optimization.
New conditions prevent gaps in optimal control problems.
problem Preventing gaps in optimal control problems with state constraints.
method Developed new sufficient conditions not relying on convexity.
result Derived bounds for the size of the relaxation gap.
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
Study KKT conditions for multi-objective optimization on Hadamard manifolds.
problem Optimizing multi-objective interval-valued functions on Hadamard manifolds.
method Developed KKT conditions for Pareto optimal solutions under different ordering and convexity notions.
result Results are more general than on Euclidean spaces.
A new model optimizes portfolios by learning stock return distributions conditioned on factors.
problem Optimizing portfolios with high-dimensional asset-specific factors.
method Conditional Diffusion Transformer architecture linking each asset's return to its factor vector.
result The model outperforms benchmarks in mean-variance and mean-CVaR optimization.
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.
Integrates estimation and optimization for uncertain parameters.
problem Optimizing with uncertain parameters whose distributions can be estimated.
method Integrated Conditional Estimation-Optimization (ICEO) framework.
result Asymptotically consistent and provides finite performance guarantees.
Improved Bayesian optimization for conditional parameter spaces.
problem Efficient global optimization of expensive-to-evaluate functions in conditional parameter spaces.
method Additive tree-structured covariance function for conditional parameter optimization.
result Significantly improved sample-efficiency and wider applicability compared to existing methods.
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.
Develops new optimization techniques for decision-making under uncertainty.
problem Decision-making under uncertainty with complex cost functions and nested expectations.
method Introduces Multistage Conditional Compositional Optimization (MCCO) and develops multilevel Monte Carlo techniques.
result New optimization techniques reduce scenario complexity from exponential to polynomial growth.
Integrates side information for robust portfolio optimization.
problem Portfolio optimization under uncertainty and side information.
method Distributionally robust optimization with optimal transport ambiguity set.
result The problem can be reformulated as a finite-dimensional optimization problem.
The paper explores conditions for predicting optimization performance.
problem Lack of formal theoretical guarantees linking prediction and optimization performance.
method Exploring conditions for asymptotic convergence and exact quantification of optimization performance.
result Explicit theoretical relationship between prediction and optimization performance.
Neural framework for conditional OT maps learns from categorical and continuous variables.
problem Learning conditional optimal transport maps between complex distributions.
method Hypernetwork generates adaptive transport layer parameters based on conditioning variables.
result Our method outperforms simpler conditioning methods in comprehensive ablation studies.
Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent may care only about states where she is still alive at the time …
Unified framework for structure learning via conditional independence testing.
problem Optimal structure learning and conditional independence testing.
method Established a fundamental connection and reduction between structure learning and conditional independence testing.
result Optimal rates for structure learning are determined by conditional independence testing rates.
Develops theory for conditional optimal transport in infinite-dimensional spaces.
problem Bayesian inference with functional parameters in infinite-dimensional spaces.
method Theory of constrained optimal transport for block-triangular maps.
result Regularity estimates on conditioning maps from prior to posterior.
Estimates conditional Brenier maps using entropic optimal transport.
problem Non-parametric estimation of conditional Brenier maps.
method Entropic optimal transport for scalable non-parametric estimation.
result Entropic optimal transport maps asymptotically converge to conditional Brenier maps.
Study proves optimal controls for stochastic Volterra equations with singular kernels.
problem Existence of optimal controls for stochastic Volterra equations with singular kernels.
method Sufficient conditions based on integrability and growth hypotheses.
result Existence of optimal relaxed and strict controls under classical convexity assumptions.
MOPI optimizes flexible set-valued mappings to achieve superior shape adaptivity in conformal prediction.
problem Challenges in achieving valid conditional coverage in conformal prediction.
method Minimax Optimization Predictive Inference (MOPI) framework that optimizes over a flexible class of set-valued mappings.
result MOPI achieves superior shape adaptivity and maintains a principled connection to mean squared coverage error.
Method learns conditional distributions using neural entropic optimal transport.
problem Challenges in learning multiple conditional distributions.
method Neural entropic optimal transport method with two networks and regularization.
result Effective learning of conditional distributions with limited samples.
Study optimality conditions for interval-valued optimization problems on Riemannian manifolds.
problem Optimizing interval-valued functions on Riemannian manifolds under a total order relation.
method Generalized Hukuhara directional differentiability to derive KKT-type optimality conditions.
result Derives optimality conditions for interval-valued optimization problems on Riemannian manifolds.
Success conditioning optimizes policies by imitating successful trajectories, solving a trust-region optimization problem.
problem Improving policies through random actions that lead to desired outcomes.
method Success conditioning, which involves collecting and updating policies based on successful trajectories.
result Success conditioning solves a trust-region optimization problem, maximizing policy improvement with a χ2 divergence constraint. New methods target conditional demographic parity using optimal transport distances.
problem Auditing and enforcing conditional demographic parity (CDP) in models with complex conditioning variables.
method Developed novel measures of conditional demographic disparity (CDD) based on optimal transport distances and regularization-based approaches.
result Validated methods airbit{} and airlp{} effectively target CDP in real-world datasets with continuous model outputs.
This paper proposes a new method for conditional sampling using optimal transport.
problem Sampling conditional distributions in Bayesian inference and density estimation.
method Iterative block-triangular transport maps solving an optimal transport problem with a weighted L2 cost function.
result The proposed method extends the data-driven approach for conditional sampling.
Optimal reinsurance contracts for multiple dependent risks are derived without specific dependency assumptions.
problem Finding optimal reinsurance contracts for multiple dependent risks without assuming their dependency structure.
method Assumes maximal expected utility criterion and independent negotiation of reinsurance for each risk. Derives optimality conditions and shows that under mild assumptions, optimal contracts are classical (non-randomized) type.
result Optimal reinsurance contracts exist and can be classical (non-randomized) type under mild assumptions.
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all these problems. A high order maximum principle (Krener, 1977) must be used in o…
Efficiently computes optimal transport maps and Wasserstein barycenters using conditional normalizing flows.
problem Computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces.
method Uses conditional normalizing flows to approximate distributions and solve the primal problem.
result Shows computational feasibility for hundreds of input distributions and yields accurate results.
Paper proposes a pre-conditioning method to speed up gradient descent in multi-agent optimization.
problem Speed up convergence of gradient descent in multi-agent optimization problems.
method Iterative pre-conditioning approach to mitigate the effect of problem conditioning.
result Significant improvement in convergence speed of gradient descent method.
Optimal model averaging for conditional generative models improves performance across various data types.
problem Multiple plausible generators for conditional distributions can vary in performance.
method Sample-based maximum mean discrepancy, static model averaging, and mixture-of-experts model averaging.
result MoEMA improves over competing baselines across various data types.
New method solves complex optimization problems with real-time learning.
problem Nonconvex nonsmooth conditional stochastic optimization problems.
method Single time-scale stochastic method with parametric model approximation.
result Method converges with probability one using differential inclusions and Lyapunov function.
Derives optimal control conditions using calculus of variations.
problem Optimizing Markov control in stochastic control problems.
method Calculus of variations approach to derive necessary conditions.
result Solves the Merton portfolio optimization problem.
We study the positivity properties of Hermitian (or even Finsler) holomorphic vector bundles in terms of Lp-estimates of ∂ˉ and Lp-extensions of holomorphic objects. To this end, we introduce four conditions, called the optimal Lp-estimate condition, the multiple coarse Lp-estimate condition, th…
We study the error landscape of deep linear and nonlinear neural networks with the squared error loss. Minimizing the loss of a deep linear neural network is a nonconvex problem, and despite recent progress, our understanding of this loss surface is still incomplete. For deep linear networks, we present necessary and s…
New algorithms improve distributed optimization under mild variance conditions.
problem Improving distributed optimization for large-scale machine learning problems.
method Revisited Federated Averaging and SCAFFOLD algorithms under a general variance condition.
result Established convergence results for smooth nonconvex objective functions under mild variance conditions.
In the problem of optimal investment with utility function defined on (0,∞), we formulate sufficient conditions for the dual optimizer to be a uniformly integrable martingale. Our key requirement consists of the existence of a martingale measure whose density process satisfies the probabilistic Muckenhoupt $(A_p…
We analyze conditional optimization problems arising in discrete time Principal-Agent problems of delegated portfolio optimization with linear contracts. Applying tools from Conditional Analysis we show that some results known in the literature for very specific instances of the problem carry over to translation invari…
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
problem Constructing minimum-volume prediction regions that satisfy conditional coverage.
method Super-level-set regression (SLS) directly optimizes geometric boundaries of conditional level sets.
result SLS optimizes regions directly, capturing complex conditional structures end-to-end.
Study optimal transport on null hypersurfaces and null energy condition.
problem Optimal transport degeneracy on null hypersurfaces.
method Developed tools to characterize null energy condition using convexity properties of entropy.
result Optimal transport characterization of null energy condition.
Study on DiTs' rates of approximation and estimation under various data assumptions.
problem Investigating statistical rates of conditional diffusion transformers.
method Discretization and Taylor expansion of conditional diffusion score function under Hölder smooth data assumption.
result Establishes statistical limits for conditional and unconditional DiTs, offering practical guidance.
New gradient methods solve multiscale optimization problems efficiently.
problem Minimizing functions with multiple non-interacting smooth, strongly convex components.
method Big-Step-Little-Step interleaving of standard methods.
result Complexity bound scales as product of square-roots of condition numbers of components, improving on accelerated gradient methods.
Classical scaling is shown to be optimal under various noisy conditions.
problem Consistency of classical scaling under general noise conditions.
method Established using finite fourth moments of noise, derived convergence rates, and matching minimax lower bounds.
result Classical scaling achieves minimax optimality in recovering true configuration from noisy dissimilarities.
This paper optimizes diagonal preconditioning to improve matrix condition numbers.
problem Optimizing diagonal preconditioning to reduce matrix condition numbers.
method Reformulated as a quasi-convex problem, solved with bisection and Newton updates.
result Optimal diagonal preconditioners can significantly improve iterative methods.
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.
The paper develops a new approach to conditional risk measures using modular convex analysis.
problem Developing a new method for conditional risk measures.
method Random modular approach to conditional certainty equivalents and niveloids in the conditional L∞-space. result Retrieves a conditional variational formula for optimized certainty equivalents and applies it to the conditional entropic risk measure.
Improved subgradient method tackles ill-conditioned composite optimization problems.
problem Slow convergence of subgradient method for composite optimization problems.
method Preconditioned subgradient method with Levenberg-Marquardt approach.
result Linear convergence rate for composite optimization problems under mild conditions.
Bayesian optimization is a class of data efficient model based algorithms typically focused on global optimization. We consider the more general case where a user is faced with multiple problems that each need to be optimized conditional on a state variable, for example given a range of cities with different patient di…
We develop the first Bayesian Optimization algorithm, BLOSSOM, which selects between multiple alternative acquisition functions and traditional local optimization at each step. This is combined with a novel stopping condition based on expected regret. This pairing allows us to obtain the best characteristics of both lo…
Develops CPL for optimal prediction set length and validity.
problem Balancing conditional validity and length efficiency in conformal prediction.
method Conformal Prediction with Length-Optimization (CPL).
result Achieves optimal prediction set length while maintaining conditional validity.