We reformulate data-dependent constraints to ensure they are always met with high probability.
problem Ensuring fairness and stability in machine learning models with data-dependent constraints.
method Calibrated reformulation of constraints to guarantee satisfaction with a specified probability.
result Our method guarantees that fairness constraints are met at test time with high probability.
Study on relativistic nonholonomic mechanics with time-dependent constraints.
problem Formulating classical time-dependent nonholonomic mechanics.
method Invariant formulation using moving frames and Chaplygin systems.
result Hamiltonization of time-dependent constraints achieved.
The constraint reaction force of ideal nonholonomic constraints in time-dependent mechanics on a configuration bundle Q→R is obtained. Using the vertical extension of Hamiltonian formalism to the vertical tangent bundle VQ of Q→R, the Hamiltonian of a nonholonomic constrained system is constructed.
Study risk aggregation with order constraint under unknown dependence.
problem Risk aggregation with an order constraint under uncertainty.
method Introduced DL coupling for concave order risk aggregation, generalized to tail risk measures.
result Analytical formulas for bounds on Value-at-Risk with improved accuracy.
ARO overfits by making constraints dependent on uncertainty, leading to brittleness.
problem ARO's adaptive policies become brittle when realizations fall outside the uncertainty set.
method Assigning constraint-specific uncertainty set sizes with probabilistic guarantees.
result Regularization through specific uncertainty set sizes ensures stability and flexibility.
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path d…
The paper solves a consumption-investment problem with state-dependent lower bounds.
problem A life-time consumption-investment problem with a state-dependent lower bound on consumption.
method Transformed the problem into a state-independent control problem to apply standard theory.
result Explicit optimal strategies provided for both homogeneous and non-homogeneous constraints.
ZNMF improves facial recognition performance using data-dependent penalties.
problem Facial recognition performance in the Cambridge ORL database.
method ZNMF uses data-dependent auxiliary constraints to modify NMF.
result ZNMF outperforms other constrained NMF algorithms in facial recognition.
We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can transmit an impulse to the motion at the points of dependence and derive an explicit fo…
This paper optimizes dividend payout rates with a drawdown constraint in a stochastic model.
problem Optimizing dividend payout rates while avoiding drawdowns in a stochastic model.
method Solving a path-dependent stochastic control problem using Hamilton-Jacobi-Bellman equations and PDE methods.
result Explicit characterization of an optimal feedback control strategy, including two free boundaries and the running maximum surplus process.
Unsupervised two-view learning, or detection of dependencies between two paired data sets, is typically done by some variant of canonical correlation analysis (CCA). CCA searches for a linear projection for each view, such that the correlations between the projections are maximized. The solution is invariant to any lin…
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these cons…
Classifiers can be trained with data-dependent constraints to satisfy fairness goals, reduce churn, achieve a targeted false positive rate, or other policy goals. We study the generalization performance for such constrained optimization problems, in terms of how well the constraints are satisfied at evaluation time, gi…
Smoothness analysis of adversarial training reveals L∞ constraints cause more non-smoothness.
problem Non-smoothness of adversarial training loss function.
method Analyzed the smoothness of adversarial training loss function using optimal attacks for model parameters.
result The L∞ constraint causes more non-smoothness than L2 constraint. New control theory for self-path-dependent problems solves unique constraints.
problem Optimal control with self-path-dependent constraints in stochastic systems.
method Introduces new HJB equations for variational inequalities with historical maximum controls.
result Value functions are viscosity solutions to HJB equations under Lipschitz conditions.
New method for private learning with fairness constraints.
problem Rate-constrained optimization under differential privacy.
method RaCO-DP, a DP variant of SGDA solving Lagrangian formulation.
result Empirical results show RaCO-DP outperforms existing methods.
New algorithm reduces regret and constraint violation in online convex optimization with complex constraints.
problem Online convex optimization with multiple functional constraints and a simple constraint set.
method Instance-dependent bound using online primal-dual mirror-prox algorithm in general normed spaces.
result Achieves an O(√V*(T)) regret and O(1) constraint violation, improving over previous works.
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we give a basis of constraint functions in the Lagrangian and Hamiltonian sides. An ad…
Proposes rounding method for precise treatment effect estimation under budget constraints.
problem Resource-constrained experimental design for precise treatment effect estimation.
method Dependent randomized rounding procedure to convert assignment probabilities into binary treatment decisions.
result Improved estimator precision through variance reduction and efficient inference.
New algorithms for constrained online optimization with memory and predictions.
problem Control of constrained dynamical systems and scheduling with reconfiguration budgets.
method Proposed algorithms achieving sublinear regret and constraint violation under time-varying constraints, both with and without predictions.
result First algorithms achieving sublinear regret and constraint violation in constrained online optimization with memory.
Bandit algorithms have various application in safety-critical systems, where it is important to respect the system constraints that rely on the bandit's unknown parameters at every round. In this paper, we formulate a linear stochastic multi-armed bandit problem with safety constraints that depend (linearly) on an unkn…
New method optimizes portfolios by dynamically integrating ESG constraints.
problem Static ESG scores mismatch sequential portfolio decisions.
method MACF-X, a family of adapters that learns ESG costs from multimodal evidence.
result Reduces tail ESG budget pressure while maintaining financial performance.
Algorithm ensures privacy while strictly adhering to constraints.
problem Differential privacy with linear constraints that must be strictly followed.
method Developed an algorithm that releases a nearly-optimal solution satisfying constraints with probability 1.
result Achieved nearly optimal performance while preserving privacy and strictly adhering to constraints.
VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.
problem Stochastic convex optimization under convex constraints.
method Natural variance reduced proximal gradient (VRPG) algorithm.
result VRPG achieves local minimax lower bound up to constants and log factor of N. A framework for analyzing financial systems under scenario constraints.
problem Quantifying worst-case and best-case performance in financial systems.
method Quantitative automata-based framework integrating event history automata and weighted finance finite automata.
result Exact calculation of upper and lower payoff bounds with interpretable witness event histories.
This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete. the prices of financial assets are modeled by Itô processes. The dynamic risk constr…
Algorithm optimizes ε-SVR with MAPE loss and sample-dependent constraints.
problem Optimizing ε-SVR with MAPE loss and sample-dependent constraints.
method Sequential Minimal Optimization (SMO) for ε-SVR with MAPE loss and sample-dependent box constraints.
result Algorithm achieves lowest median runtime on every tested configuration.
We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization. Unlike most CD methods, we do not assume the constraints to be separable, but let them be coupled linearly. To our knowledge, ours is the first CD method that allows linear coupling constraints, without making th…
Study optimal consumption with drawdown limits over a fixed time frame.
problem Maximizing utility with consumption limits during a fixed period.
method Extended utility maximization problem with drawdown constraint, using PDE arguments and dual transform.
result Existence and uniqueness of classical solution to HJB variational inequality, with explicit free boundaries.
Paper proves conditions for estimating precision matrices with Laplacian constraints.
problem Estimating high-dimensional precision matrices with Laplacian constraints.
method Minimizing Stein's loss with conditions on graph connectivity and Laplacian constraints.
result High-dimensional consistency achieved with Laplacian constraints, independent of graph structure.
Simplifies neural network constraints with computationally efficient method.
problem Implementing hard output constraints in neural networks.
method Additional neural network layer for output constraints.
result Computational simplicity with complexity O(n*m) for linear constraints.
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
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.
Adaptive allocation with constraints using Thompson sampling.
problem Choosing allocations repeatedly with unknown returns and constraints.
method Thompson sampling approach with finite-sample regret bound.
result Prior-independent bound on expected regret for exponential allocations.
SnareNet adds repair layers to neural networks to ensure outputs meet physical constraints.
problem Unconstrained neural network predictions violate physical or safety requirements.
method SnareNet appends a differentiable repair layer that navigates constraints to produce feasible outputs.
result SnareNet consistently improves objective quality while satisfying constraints more reliably.
New neural network models extreme value distributions with preserved shape constraints.
problem Modeling multivariate extreme value distributions with preserved shape constraints.
method d-max-decreasing neural network architecture for non-parametric calibration and generation of MEVs.
result The proposed architecture approximates the dependence structure of MEVs at parametric rate and preserves essential shape constraints.
We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the …
Hybrid quantum algorithm tackles binary optimization problems with multiple constraints.
problem Efficiently solving binary optimization problems with multiple constraints using quantum algorithms.
method Combines QAOA with penalty dephasing and Zeno effect for non-Ising constraints.
result Significant improvement in solving practical aircraft loading problems.
Previous studies into the budget constraint of portfolio optimization problems based on statistical mechanical informatics have not considered that the purchase cost per unit of each asset is distinct. Moreover, the fact that the optimal investment allocation differs depending on the size of investable funds has also b…
New loss function handles uncertain constraints in CSLO problems.
problem Handling uncertain inequality constraints in CSLO with machine learning predictions.
method Introduces SPO-RC loss and SPO-RC+ surrogate, trains on truncated datasets, corrects bias.
result SPO-RC+ effectively manages constraint uncertainty and improves performance.
Many applications of AI involve scoring individuals using a learned function of their attributes. These predictive risk scores are then used to take decisions based on whether the score exceeds a certain threshold, which may vary depending on the context. The level of delegation granted to such systems in critical appl…
ACOL learns constraints from human preferences in driving simulations.
problem Learning constraints from human preferences in driving simulations.
method Adaptive Constraint Learning (ACOL) algorithm for constrained linear best-arm identification.
result ACOL's sample complexity matches worst-case lower bound and is significantly tighter in the average case.
Improved sample complexity for ReLU networks with norm constraints.
problem Estimating sample complexity for ReLU networks under norm constraints.
method Refined Rademacher complexity analysis for function class.
result Often no explicit depth-dependence in sample complexity bound.
Bayesian models use hyperparameters to indirectly assign priors, and this work shows how these priors can be derived from maximum entropy principles.
problem Understanding the assumptions and dependencies in Bayesian hierarchical models.
method Demonstrates how canonical distributions and maximum entropy principles can be used to derive marginal priors in hierarchical models.
result Marginal priors in hierarchical models derived from maximum entropy principles have different constraints compared to the original priors.
New NMF algorithm uses Toeplitz matrix for facial recognition.
problem Facial recognition performance improvement.
method Proposes TNMF algorithm with Toeplitz penalty for NMF.
result TNMF outperforms ZNMF and other constrained NMF algorithms.
New methods for efficient exploration under unknown linear constraints in bandits.
problem Optimizing decisions under unknown linear constraints in bandit problems.
method Lagrangian relaxation, computationally efficient extensions of existing methods, constraint-adaptive stopping rule.
result LAGEX achieves asymptotically optimal sample complexity, LATS shows asymptotic optimality up to novel constants.
We consider the problem of learning Markov Random Fields (including the prototypical example, the Ising model) under the constraint of differential privacy. Our learning goals include both structure learning, where we try to estimate the underlying graph structure of the model, as well as the harder goal of parameter l…
We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term ρ-arbitrage for a risk measure ρ. We show how to determine analytically whether such ρ-ar…