We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning algorithms, where we argue that the objective, validation error, can be decomposed as mono…
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48 results for “monotonic optimization”
Bayesian optimization with preference learning using monotonic neural networks.
problem Optimizing complex systems with multiple conflicting objectives.
method Proposes a neural network ensemble for utility surrogate modeling, leveraging monotonicity.
result Demonstrates superior performance compared to existing methods.
Monotonic differentiable sorting networks improve upon previous methods.
problem Non-monotonicity in differentiable sorting networks.
method Relaxation of conditional swap operations using sigmoid functions to ensure monotonicity.
result Monotonic differentiable sorting networks improve upon previous methods.
New algorithm solves composite optimization problems with unknown expectations.
problem Solving composite optimization problems with unknown statistical expectations.
method Proposes a new stochastic primal-dual algorithm for composite optimization problems with unknown statistical expectations.
result Converges to a saddle point of the Lagrangian function.
Study online monotone density estimation with expert aggregation and log-optimal calibration.
problem Online monotone density estimation and log-optimal calibration.
method Proposed two online estimators: Grenander estimator and expert aggregation estimator.
result Online estimators achieve cumulative log-likelihood gap and pathwise regret bound.
Efficient, Anytime Algorithms for Calibration with Isotonic Regression under Strictly Convex Lossescs.LG
Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.
problem Calibrating estimations to improve performance with monotone transforms.
method Proposed linear-time and space algorithm for finding optimal monotone transforms for specific loss functions. Also proposed an anytime algorithm with linear space and pseudo-linearithmic time complexity.
result Optimal monotone transforms are unique and can be found efficiently for various strictly convex loss functions.
Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences-Stochastic Factor Caseq-fin.PM
We consider an incomplete market with a nontradable stochastic factor and a continuous time investment problem with an optimality criterion based on monotone mean-variance preferences. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to find an optimal investmen…
Monotone adversarial corruptions degrade optimal learning algorithms.
problem Optimal learning algorithms' reliance on exchangeability and independence is challenged.
method Introduces a monotone adversarial corruption model where an adversary adds monotone corruptions to a clean dataset.
result Optimal learning algorithms achieve suboptimal expected error on new test points.
The paper tackles online learning problems with monotone arm sequences, achieving optimal or near-optimal regret bounds.
problem Online learning problems with ordinal and monotone arm sequences, such as dynamic pricing and clinical trials.
method Proposes algorithms for continuum-armed bandit problems with monotone arm sequences, achieving optimal or near-optimal regret bounds.
result Achieves optimal or near-optimal regret bounds for monotone arm sequences, differing from the continuous-armed bandit literature.
This work shows MLPs can approximate monotonic functions without bounded activations.
problem Optimizing MLPs with monotonic constraints and bounded activations.
method Generalized theoretical results showing MLPs with non-negative weights and saturating activations are universal approximators.
result MLPs with non-negative weights and saturating activations are universal approximators for monotonic functions.
This paper introduces a novel monotone curve estimation framework based on convex duality.
problem Estimating smooth, continuous, and monotonic curves in data.
method Convex duality and optimal transport theories.
result Established statistical guarantees for monotone curve estimates.
Study solves optimal portfolio selection using HJB equation.
problem Optimal portfolio selection problem.
method Maximal monotone operator method, Banach fixed-point theorem, Fourier transform, monotone operators technique.
result Existence and uniqueness of solution to HJB equation.
Paper investigates monotonicity issues in AI preference learning.
problem AI models may violate monotonicity when learning preferences.
method Investigates root causes of non-monotonicity in comparison-based preference learning.
result Proves local pairwise monotonicity under mild assumptions.
Researchers propose a non-monotone quantum natural gradient for quantum systems.
problem Applying natural gradient methods to quantum systems without monotonicity.
method Introducing a non-monotone quantum natural gradient (QNG) and demonstrating its superiority over conventional QNG.
result Non-monotone QNG outperforms conventional QNG in terms of convergence speed.
Developed a monotone numerical method for MV portfolio optimization under jump-diffusion models.
problem Efficiently optimizing portfolios with jump-diffusion dynamics and investment constraints.
method Strictly monotone numerical integration method using Fourier transforms and composite quadrature rules.
result Proven to be -stable and pointwise consistent, converging to the MV optimization solution.
Study optimal portfolio allocation in a general semimartingale model.
problem Dynamic optimal portfolio allocation under monotone mean-variance preferences.
method New results in semimartingale theory applied to Sharpe ratio analysis.
result Characterization of circumstances for improving mean-variance efficiency.
Brenier Isotonic Regressionstat.ML
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
The paper examines properties of GW optimal transport plans, showing they can be sparse and permutation-supported.
problem Properties of Gromov-Wasserstein optimal transport plans.
method Exploration of sparsity, permutation support, and cyclical monotonicity properties.
result GW optimal plans can be sparse and permutation-supported under certain conditions.
The paper solves MMV and MV problems with random coefficients and finds shared optimal strategies.
problem Optimal trading strategies with random market coefficients.
method Backward stochastic differential equations (BSDEs) to find optimal strategies.
result MMV and MV problems share the same optimal portfolio and value under random coefficients.
We propose learning deep models that are monotonic with respect to a user-specified set of inputs by alternating layers of linear embeddings, ensembles of lattices, and calibrators (piecewise linear functions), with appropriate constraints for monotonicity, and jointly training the resulting network. We implement the l…
Pairwise counter-monotonicityq-fin.RM
Study on pairwise counter-monotonicity, a type of negative dependence.
problem Understanding and quantifying extremal negative dependence structures.
method Established stochastic representation and invariance property; showed implications and connections.
result Pairwise counter-monotonicity implies negative association and joint mix dependence.
The paper analyzes Variable Annuities with surrender charges, providing a pricing formula and optimal exercise boundary.
problem Analyzing Variable Annuities with surrender charges and early termination rights.
method Formulated as an optimal stopping problem with a discontinuous payoff, non-monotonic optimal stopping boundaries are proven continuous and regular.
result A rigorous pricing formula and optimal exercise boundary for surrender options are derived.
Paper solves a control problem with robust methods.
problem Monotone mean-variance problems with stochastic coefficients.
method Finding saddle point through BSDEs with unbounded coefficients.
result Optimal control and value match mean-variance problems.
Paper tackles stochastic -submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of -submodular functions with full-bandit feedback.
method Proposes online algorithms for various -submodular stochastic combinatorial multi-armed bandit problems.
result Achieves sublinear -regret bounds for multiple -submodular stochastic combinatorial multi-armed bandit problems.
New proof of energy functional monotonicity via geodesics in measure space.
problem Proving monotonicity of energy functional in generalized Ricci flow.
method Defining adapted cost functional, geodesics, and entropy functional.
result Monotonicity of cost along backwards heat flow and energy functional along generalized Ricci flow.
The paper develops algorithms to restore monotonicity in non-monotone functions.
problem Non-monotone solutions from heuristic algorithms need to be corrected.
method Develops algorithms to restore monotonicity with limited queries.
result Restores monotonicity while degrading the function value by at most ε.
We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod e…
Learning Variational Inequalities from Data: Fast Generalization Rates under Strong Monotonicitycs.LG
This paper shows how to learn variational inequalities fast with strong monotonicity.
problem Learning variational inequalities efficiently.
method Extending convex optimization techniques to variational inequalities with strong monotonicity.
result Fast generalization rates of for learning variational inequalities.
The paper studies risk-sharing allocations for risk-seeking agents using a common distortion risk measure.
problem Characterizing Pareto-optimal risk-sharing allocations for risk-seeking agents.
method Modeling preferences with a common distortion risk measure and analyzing three settings: risk-averse, risk-seeking, and inverse S-shaped distortion.
result Pareto-optimal allocations for risk-seeking agents are counter-monotonic, not comonotonic.
This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint, and then in a Markovian…
Plateau in Monotonic Linear Interpolation -- A "Biased" View of Loss Landscape for Deep Networksstat.ML
The monotonic linear interpolation in deep networks often leads to plateaus, revealing biases in optimization.
problem Plateaus in the optimization landscape of deep networks during monotonic linear interpolation.
method Investigated monotonic linear interpolation on deep neural networks, focusing on biases in weights and biases.
result Interpolating weights and biases differently can lead to significant differences in loss and accuracy, revealing biases in optimization.
The paper characterizes optimal dynamic portfolios for a modified mean-variance utility.
problem Optimal dynamic portfolio choice for a modified mean-variance utility.
method Complete characterization under minimal assumptions, no restrictions on asset return moments.
result Maximal MMV utility is linked to the monotone Sharpe ratio, with global squared MSR as the nominal yield.
Higher-order methods for convex-concave min-max optimization and monotone variational inequalitiesmath.OC
Improved algorithms for convex-concave min-max optimization and monotone variational inequalities.
problem Efficiently solving constrained convex-concave min-max problems and monotone variational inequalities.
method Higher-order methods achieving iteration complexities of O(1/T^{ rac{p+1}{2}}) for p-th order derivatives.
result Achieved improved convergence rates for min-max and monotone variational inequalities.
In this note we will adapt Topping's -optimal transportation theory for Ricci flow to a more general situation, i.e. to a closed manifold evolving by , where is a symmetric tensor field of (2,0)-type on . We extend some recent results of Topping, Lott …
Monotonic policy improvement and off-policy learning are two main desirable properties for reinforcement learning algorithms. In this paper, by lower bounding the performance difference of two policies, we show that the monotonic policy improvement is guaranteed from on- and off-policy mixture samples. An optimization …
New method calibrates neural network predictions for better reliability.
problem Improper probability estimates from deep networks leading to unreliable predictions.
method Proposes a constrained optimization approach for a monotonic calibration map.
result Achieves state-of-the-art performance across various datasets and models.
Bayesian optimization improves Monte-Carlo tree search for better state value estimation.
problem Slow convergence in Monte-Carlo tree search due to averaging in backpropagation.
method Softmax MCTS and Monotone MCTS, using Bayesian optimization with Gaussian process prior.
result Our framework outperforms previous methods in computer Go.
Two new algorithms solve high-dimensional optimization problems without gradients.
problem Optimizing complex, high-dimensional functions without gradient information.
method GradientLess Descent (GLD) algorithms that use evaluations at adaptively chosen inputs.
result Converges within an ε-ball of the optimum with a number of evaluations that is poly-logarithmic in dimensionality.
Monotone 2D Integration Scheme for Mean-CVaR Optimization via Fourier-Trained Transition Kernelsmath.OC
New method for optimizing risk in financial models using Fourier transforms.
problem Optimizing risk in financial models with multi-period mean-CVaR.
method Strictly monotone 2D integration scheme via Fourier-trained transition kernels.
result Established robust and accurate optimization method for financial models.
New method for conditional sampling using M-GANs, likely-free inference.
problem Conditional sampling of probability measures.
method Developed a novel computational approach called M-GANs based on block triangular transport.
result Accurate sampling of conditional measures in various applications.
Paper tackles non-monotone DR-submodular maximization with approximation and regret guarantees.
problem Maximizing non-monotone DR-submodular functions over specific sets.
method Frank-Wolfe algorithm for general convex sets, Stochastic Gradient Ascent for down-closed convex sets.
result First approximation guarantees for both offline and online settings.
A new algorithm finds minimizers in dueling optimization with a monotone adversary.
problem Finding minimizers in dueling optimization with a monotone adversary.
method Introduces and studies dueling optimization with a monotone adversary, designs an efficient randomized algorithm.
result Efficient algorithm incurs cost and iteration complexity , asymptotically optimal.
The paper addresses risk sharing and variability measures among agents with general risk preferences.
problem Risk sharing and variability measures among agents with general risk preferences.
method Characterizes Pareto-optimal allocations using Gini deviation, mean-median deviation, and inter-quantile difference as variability measures.
result Optimal allocations are not comonotonic and feature a mixture of pairwise counter-monotonic structures.
Paper uses deep learning for accurate, monotonic cardinality estimation.
problem Accurate and monotonic cardinality estimation for similarity selection.
method Feature extraction to Hamming space, followed by deep learning regression.
result Demonstrates improved query optimizer performance.
New method identifies causal order without sparsity assumptions.
problem Causal order discovery in observational data.
method Sequential procedure to directly identify causal order.
result Direct identification of causal order without sparsity assumptions.
The paper defines new geometric concepts on Riemannian manifolds and applies them to optimization problems.
problem Optimization problems on Riemannian manifolds.
method Strongly geodesic preinvexity, strongly η-invexity, and strongly invariant η-monotonicity definitions.
result Characterization of strict η-minimizers and solutions to variational like-inequality problems.
Monotonic relationship found between in-distribution and out-of-distribution performance.
problem Understanding performance of machine learning models under distribution shifts.
method Analyzing ridge-regularized models and linear inverse problems under covariate shift.
result Monotonic relationship between in-distribution and out-of-distribution performance for certain models.
Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizonmath.PR
Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.
problem Optimal stopping problems with finite-time horizon and state-dependent discounting.
method Linear diffusion process, time-homogeneous gain function, fine regularity properties, continuity and strict monotonicity proof.
result Proves continuity and strict monotonicity of the optimal stopping boundary under mild assumptions.