Improves k-NN for monotonic data with robustness against noise.
problem Class noise in real-life data violates monotonic constraints in k-NN.
method Monotonic Fuzzy k-NN (MonFkNN) with new fuzzy membership calculation.
result Significant accuracy improvements and robustness against monotonic noise.
This paper benchmarks monotone-constrained models for credit PD across datasets and finds constraints are mostly costless.
problem Aligning machine learning model behavior with domain knowledge in credit risk.
method Benchmarked monotone-constrained versus unconstrained gradient boosting models across five datasets and three libraries, defining the Price of Monotonicity (PoM) as the relative change in AUC.
result Monotonicity constraints are almost costless on large datasets and most costly on smaller datasets, with PoM ranging from essentially zero to about 2.9 percent.
Additive Gaussian process framework handles monotonicity constraints in high dimensions.
problem Handling monotonicity constraints in high-dimensional data.
method Additive Gaussian process framework with MaxMod algorithm for dimension reduction.
result Framework enables to satisfy monotonicity constraints everywhere in the input space.
COMET learns monotonic neural networks by incorporating counterexamples.
problem Enforcing monotonicity constraints in neural networks for real-world tasks.
method Counterexample-guided learning technique for ReLU neural networks.
result COMET achieves state-of-the-art results and improves model quality.
Paper tackles stochastic k-submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of k-submodular functions with full-bandit feedback. method Proposes online algorithms for various k-submodular stochastic combinatorial multi-armed bandit problems. result Achieves sublinear α-regret bounds for multiple k-submodular stochastic combinatorial multi-armed bandit problems. Study finds equivalence between MMV and MV preferences with conic constraints.
problem Monotone mean-variance portfolio selection under conic constraints.
method Closed-form solutions for optimal strategies under MMV and MV preferences.
result Optimal strategies coincide with and without the conic constraint.
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.
New algorithm maximizes non-monotone adaptive submodular functions in linear time.
problem Maximizing non-monotone adaptive submodular functions subject to a cardinality constraint.
method Developed a linear-time algorithm for non-monotone adaptive submodular maximization.
result Achieved a 1/e−ε approximation ratio with O(nε−2logε−1) value oracle queries. Novel framework for efficient Gaussian process models with monotonicity constraints.
problem Improving predictive accuracy and reducing uncertainty in high-dimensional problems with monotonicity constraints.
method Virtual point-based framework using regularized linear randomize-then-optimize (RLRTO) and No U-Turn Sampler (NUTS) for efficient sampling.
result Significant improvements in computational efficiency with the RLRTO method and NUTS enhancements.
Two new methods improve monotonic constraint enforcement in regression and classification trees.
problem Improving monotonic constraints in regression and classification trees.
method Proposed two new methods: one yields better results than LightGBM, the other yields even better results but is slower.
result The best method consistently beats the current implementation of LightGBM, achieving up to 1% loss reduction.
Productivity and credit limits affect aggregate production in non-monotonic ways.
problem Understanding how aggregate production is influenced by individual characteristics and financial constraints.
method Analytical proof of non-monotonic effects of productivity and credit limits on aggregate production in a general equilibrium model.
result Equilibrium aggregate production can be non-monotonic in both individual productivity and credit limit.
Differentially private algorithms for submodular maximization under various constraints.
problem Maximizing decomposable submodular functions under constraints while preserving privacy.
method Designing differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints.
result Improved utility guarantees and competitive performance compared to non-private algorithms.
Monotonic neural networks have recently been proposed as a way to define invertible transformations. These transformations can be combined into powerful autoregressive flows that have been shown to be universal approximators of continuous probability distributions. Architectures that ensure monotonicity typically enfor…
Algorithm reduces regret in safe Bayesian optimization with monotonicity constraints.
problem Sequentially maximize unknown function with safety constraints.
method Sequential algorithms using Gaussian processes with safety constraints modeled as monotonicity.
result Sublinear regret achieved for expanding safe region and finding optimal s. Kernel-based tests for shape constraints in finance.
problem Enforcing shape relations on latent functions in financial econometrics.
method Kernel-based nonparametric framework for mean-variance optimization.
result Established statistical properties and a joint Wald-type statistic for testing shape constraints.
When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative monotonicities was formally represented and incorporated into learning algorithms (e…
A new GP method enforces physical constraints in probabilistic terms.
problem Unbounded model in GP regression leading to infeasible values.
method Introduces a new GP method using QHMC to enforce soft inequality and monotonicity constraints.
result Improves accuracy and reduces variance in GP model.
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…
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…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty. W…
FISAR uses neural networks to optimize safe reinforcement learning with forward-invariant constraints.
problem Safe reinforcement learning with constraints in safety-critical environments.
method Imposing linear constraints on policy parameters' updating dynamics, using a DNN-based optimizer to satisfy these constraints.
result The policy decreases constraint violation and maximizes cumulative reward monotonically.
A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.
problem Solving variational inequality problems with multiple functional constraints efficiently.
method Constrained Gradient Method (CGM) for Minty variational inequality problems.
result The Constrained Gradient Method achieves complexity similar to projection-based methods but with cheaper oracles.
Motivated by the problem of optimal portfolio liquidation under transient price impact, we study the minimization of energy functionals with completely monotone displacement kernel under an integral constraint. The corresponding minimizers can be characterized by Fredholm integral equations of the second type with cons…
Non-affine aggregation rules cannot preserve monotonicity in convex learning.
problem Designing non-affine aggregation rules that maintain monotonicity in convex learning.
method Proving that monotonicity of aggregated gradients is preserved only if the aggregation rule is positively affine.
result Non-affine aggregation prevents steady convergence and substantially degrades algorithmic stability.
Study best arm identification with safety constraints in bandit problems.
problem Real-world decision-making with safety constraints.
method Analyzed linear and monotonic reward and safety constraints, proposed algorithms.
result Guaranteed safe learning in both linear and general reward/safety constraint settings.
Develops a first-order interior-point method for solving constrained variational inequalities.
problem Solving constrained variational inequalities with nontrivial constraints.
method ADMM-based interior-point method for constrained VIs (ACVI).
result First-order interior-point method with global convergence guarantees for general cVI problems.
Study optimal execution in financial markets with constraints.
problem Optimal execution with non-negative constraints in a linear price impact model.
method Purely probabilistic approach via non-linear ODE.
result Complete characterization of value and optimal control.
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Sev…
Survey of Gaussian process constraints for modeling expensive data.
problem Modeling expensive data with physical constraints.
method Overview of various Gaussian process constraints and their implementation.
result Discussion of computational challenges introduced by constraints.
This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear. Adding those constraints into the problem allows to add prior knowledge on the estimator obtained, such as finding probability vector or monotone data. We propose a generalization of the Sequential Mi…
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.
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their applicability remains limited when the problem dimension is large and the projecti…
The paper studies how arm selection in a bandit problem changes with shape constraints.
problem Stochastic Thresholding Bandit Problem under shape constraints.
method Investigation of TBP under four shape constraints: monotonic increasing, unimodal, concave, and fixed.
result Minimax rates for regret vary significantly depending on the shape constraint.
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…
Introduces nondecreasing rank for matrices and tensors, developing methods and applications.
problem Finding low-rank approximations for matrices and tensors with monotonic constraints.
method Developed a variant of hierarchical alternating least squares algorithm for finding low ND rank approximations.
result Low ND rank factorizations can be found and interpreted for real-world datasets.
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance funct…
Controller-Augmented Hidden Markov Models (CHMMs) are a framework for constrained sequential inference.
problem Hidden Markov models fail under pathwise constraints like precedence, visitation, or monotonic state progression.
method CHMMs compile constraints into finite-state controllers, then use standard forward-backward and Viterbi recursions to compute exact constrained posteriors and paths.
result CHMMs provide exact constrained inference, monotone ascent in constrained EM, and linear complexity in controller cardinality.
The paper tackles robust submodular maximization under matroid constraints, providing approximation algorithms for summary extraction.
problem Maximizing submodular functions while ensuring high value even after deletions.
method Constant-factor approximation algorithms for centralized and streaming settings, considering both non-monotone and monotone objectives.
result Approximation algorithms with space complexity depending on matroid rank and deleted elements, achieving improved factors in monotone cases.
This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both investment and consumption strategies, and model uncertainty on both drift and volatil…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations are unknown but revealed across time through i.i.d. realizations. The proposed al…
Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied to any pre-trained prediction rule, while the second method deals specifically w…
Dynamic submodular maximization with consistency constraints.
problem Maximizing submodular functions in a streaming environment with limited changes.
method Algorithms with trade-offs between consistency and approximation quality.
result Effective algorithms for real-world applications.
New method tackles adversarial sign-corrupted isotonic regression, estimating monotonic signals under heavy dependence.
problem Estimating monotonic signals when responses are sign-corrupted and adversarially designed to violate monotonicity.
method Developed ASCIFIT, a three-step estimation procedure using PAVA with pre- and post-processing corrections.
result Theoretical guarantees of sharp high probability upper bounds and minimax lower bounds for ASCIFIT.
Study optimal investment-reinsurance strategy for insurers under random coefficients and jumps.
problem Optimal investment-reinsurance strategy for insurers with random coefficients and jumps.
method Solves backward stochastic differential equations with jumps under a convex cone constraint.
result Optimal strategy and value remain the same even with random coefficients and jumps.
A new method for optimal transport using neural ODEs that preserves marginal constraints.
problem Optimal transport between two continuous distributions with specific cost functions.
method Iterative construction of neural ODEs to minimize transport cost while preserving marginal constraints.
result Monotonic interior approach that decreases transport cost efficiently.
New framework for decentralized optimization of upper-linearizable functions with improved regret and complexity.
problem Decentralized optimization of upper-linearizable functions with general constraints.
method Decentralized projection-free optimization with upper-linearizable function framework.
result Regret of O(T1−θ/2) with communication complexity of O(Tθ) and linear optimization calls of O(T2θ). In this paper, we study a certain class of online optimization problems, where the goal is to maximize a function that is not necessarily concave and satisfies the Diminishing Returns (DR) property under budget constraints. We analyze a primal-dual algorithm, called the Generalized Sequential algorithm, and we obtain t…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives of a given order are subject to inequality or equality constraints. We then chara…