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.
Optimizes resource allocation in MAB models with resource constraints.
problem Optimizing resource allocation under limited and replenishing resources.
method Derives asymptotic lower bounds and constructs optimal policies.
result Achieves optimal regret for feasible uniformly fast policies.
Proposes a recursive MPC scheme with probabilistic safety guarantees for uncertain dynamic systems.
problem Probabilistic safety guarantees for MPC in dynamic environments with unknown stochastic agents.
method Uses conformal prediction to derive high-confidence prediction regions and gradually relax safety constraints online.
result Ensures recursive feasibility of MPC schemes by relaxing safety constraints over time.
We develop asymptotically optimal policies for the multi armed bandit (MAB), problem, under a cost constraint. This model is applicable in situations where each sample (or activation) from a population (bandit) incurs a known bandit dependent cost. Successive samples from each population are iid random variables with u…
New methodology optimizes complex systems design trade-offs.
problem Complex multi-objective optimization with unknown feasibility constraints.
method Introduces HyperMapper 2.0 for multi-objective optimization, handling categorical/ordinal variables.
result HyperMapper 2.0 provides better Pareto fronts and 8x improvement in sampling budget.
Algorithm ensures safe optimization under unknown constraints.
problem Optimization under unknown safety constraints.
method Reliable Frank-Wolfe (Reliable-FW) algorithm for non-convex functions.
result Algorithm finds approximate first-order stationary points safely.
The paper tackles identifying Pareto Set with constraints using bandit feedback.
problem Identifying the Pareto Set under feasibility constraints in a multivariate bandit setting.
method Fixed-confidence identification algorithm that outperforms existing methods.
result The sample complexity of the proposed algorithm is near-optimal.
New bounds for learning near-optimal policies in CMDPs with constraints.
problem Optimizing policies in CMDPs with constraints.
method Model-based algorithm addressing relaxed and strict feasibility.
result Near-optimal sample complexity bounds for CMDPs.
COF algorithm minimizes cost in multi-armed bandits with known costs and reward constraints.
problem Minimizing cost while meeting a minimum reward requirement in uncertain environments.
method COF algorithm that intelligently combines samples from all arms to gauge feasibility and minimize cost.
result COF achieves instance-dependent upper bounds on cumulative cost and quality regret.
Efficient learning-based MPC for unknown nonlinear systems with state constraints.
problem Control of discrete-time nonlinear systems with unknown dynamics and state constraints.
method Receding horizon reinforcement learning (r-LPC) using Koopman operator-based prediction model.
result Proven closed-loop recursive feasibility, robustness, and asymptotic stability under function approximation errors.
Safe linear bandits over unknown polytopes avoid safety violations and suboptimal actions.
problem Online approach to linear programming with unknown constraints and risks.
method Doubly-optimistic strategy (DOSS) for safe linear bandits over polytopes.
result DOSS achieves tight bounds on efficacy regret and safety violations.
Algorithm minimizes regret in multi-criteria bandits with constraints.
problem Optimize primary attribute while respecting secondary constraints.
method Con-LCB algorithm that guarantees logarithmic regret and feasibility identification.
result Logarithmic regret and feasibility identification with high probability.
Bayesian search optimizes exploration of feasible solutions under expensive constraints.
problem Identifying feasible solutions in computationally expensive constraint spaces.
method Bayesian models with an acquisition function for efficient exploration and exploitation.
result The proposed acquisition function improves the prediction of feasibility.
Comonotonic allocations are restored under certain constraints, improving risk-sharing.
problem Feasibility constraints can distort optimal risk-sharing allocations.
method Identified componentwise convex-order solidity as a sufficient condition to restore comonotonic allocations.
result Componentwise convex-order solidity ensures comonotonic improvements under feasible constraints.
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.
Novel algorithm improves feasibility classification of complex simulation outcomes.
problem Determining feasible regions in complex simulation environments with binary outcomes.
method Iterative exploration using machine learning techniques (kernel support vector machines, kernel ridge regression).
result Improves feasibility classification and guides exploration towards regions of interest.
Paper addresses feasibility of counterfactual explanations in ML models, especially for critical domains.
problem Feasibility of counterfactual examples in ML models, especially in healthcare and finance.
method Uses partial structural causal models and modified variational autoencoder loss to generate counterfactuals that satisfy feasibility constraints.
result Generated counterfactuals better satisfy feasibility constraints than existing methods.
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…
DC3 uses deep learning to solve hard-constrained optimization problems efficiently.
problem Hard constraints in optimization problems make classical solvers slow and infeasible.
method DC3 employs a differentiable procedure to enforce feasibility and unrolls corrections for inequality constraints.
result DC3 achieves near-optimal solutions while maintaining feasibility in both synthetic and real-world tasks.
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex sets. We propose a class of algorithms that perform both stochastic gradient desce…
New algorithm reduces regret and constraint violation in constrained bandit problems.
problem Optimizing under budget and stochastic constraints in resource-constrained settings.
method Lyapunov optimization methodology, t L y O n { t LyOn} t L y O n algorithm. result Achieves O ( K B log B ) O(\sqrt{K B\log B}) O ( K B log B ) regret and zero constraint-violation for large B B B . Unified framework for constrained online decision-making.
problem Sequential decisions under stage-wise feasibility constraints.
method Upper counterfactual confidence bounds and generalized eluder dimension.
result Principled foundation for constrained sequential decision-making.
SFLS method finds feasible solutions faster with less data.
problem Efficiently solving SOECs with near-feasibility and near-optimality.
method SFLS method that emphasizes feasibility before convergence.
result SFLS maintains high-probability feasibility at each iteration.
Geometric theory explains substitutability in market outcomes based on production constraints.
problem Understanding substitutability in markets with structured feasible products.
method Modeling the set of feasible products as a compact Riemannian manifold to study intrinsic geometry and its effects on substitutability.
result Intrinsic geometry of the feasible set governs substitutability and market outcomes, with curvature controlling technological substitution elasticity.
Algorithm minimizes regret while adhering to unknown safety constraints.
problem Online learning with unknown safety constraints.
method General meta-algorithm leveraging online regression and learning oracles.
result Concrete algorithm with T \sqrt{T} T regret for linear constraints. We define and compute plausible counterfactual explanations using density constraints.
problem Efficiently compute plausible counterfactual explanations for machine learning models.
method Propose and study a formal definition of plausible counterfactual explanations, use density estimators, and introduce convex density constraints.
result Convex density constraints ensure plausible and feasible counterfactual explanations.
Bayesian method approximates intractable stochastic programs with chance constraints.
problem Designing systems with stochastic constraints and chance constraints.
method Variational Bayesian approach to approximate posterior predictive integral.
result The solution set converges to the true solution set as the number of observations increases.
Many engineering problems require identifying feasible domains under implicit constraints. One example is finding acceptable car body styling designs based on constraints like aesthetics and functionality. Current active-learning based methods learn feasible domains for bounded input spaces. However, we usually lack pr…
A scalable method for deep metric learning using chance constraints.
problem Improving deep metric learning by addressing feasibility issues.
method Relating DML to chance constraints, reformulating as a feasibility problem, and iteratively training proxies.
result The method effectively improves deep metric learning performance across multiple benchmarks.
Develops a new framework for integrating satellite allocations in small portfolios.
problem Feasibility constraints in small portfolios, not return predictability, are the primary concerns.
method A four-layer feasibility framework: physical, economic, structural, and epistemic.
result Closed-form feasibility bounds on satellite size, turnover, and breadth without return forecasts.
Study tests feasibility of linear programs with bandit feedback.
problem Testing feasibility of unknown linear programs with bandit feedback.
method Developed a novel test based on low-regret algorithms and a nonasymptotic law of iterated logarithms.
result Proved that the test is reliable and adapts to the signal level, with mean sample costs scaling as \( \widetilde{O}(d^2/Γ^2) \).
Iterative method learns unknown constraints for MPC control.
problem Learning to satisfy unknown polyhedral state constraints in iterative MPC.
method Collects and improves estimates of unknown constraints using collected data, designs an MPC controller to satisfy the estimated constraints.
result Robust and probabilistic guarantees of constraint satisfaction as a function of task iterations.
New algorithms optimize constrained problems faster, avoiding full set optimization.
problem Optimizing constrained problems efficiently and quickly.
method Designing accelerated first-order algorithms that avoid full set optimization.
result Proved convergence to stationary points in nonconvex settings and accelerated rates in convex settings.
New algorithm finds best feasible arm in grouped bandits.
problem Finding the best arm with all attributes above a threshold.
method Feasibility Constrained Successive Rejects (FCSR) algorithm.
result FCSR identifies the best feasible arm with optimal dependence on problem parameters.
Safe learning in uncertain systems with state measurements and optimization.
problem Safe learning in nonlinear control-affine systems with unknown additive uncertainty.
method Model uncertainty as Gaussian noise, learn mean and covariance, use optimization to adjust control input.
result Guaranteed safety with arbitrarily large probability while learning and control proceed simultaneously.
The paper introduces GAER to assess market feasibility under geopolitical and institutional constraints.
problem Feasibility of adaptive market efficiency under heterogeneous institutional and geopolitical conditions.
method Structural framework integrating adaptive market theory, institutional economics, and political economy.
result GAER as a diagnostic indicator for portfolio construction feasibility.
New algorithm reduces sample complexity for constrained MDPs.
problem Learning policies in constrained average-reward MDPs.
method Model-based algorithm for relaxed and strict feasibility settings.
result Achieves minimax-optimal bounds for constrained MDPs.
Consistent algorithms for multiclass learning with complex metrics and constraints.
problem Learning with complex performance metrics and constraints.
method General framework for designing consistent algorithms by viewing the problem as an optimization over feasible confusion matrices.
result Rates of convergence to the optimal (feasible) classifier, showing asymptotic consistency.
CoCoRL learns safe constraints from demonstrations with unknown rewards.
problem Learning safe constraints from demonstrations with different unknown rewards.
method Convex Constraint Learning for Reinforcement Learning (CoCoRL) constructs a convex safe set based on demonstrations.
result CoCoRL learns constraints that lead to safe driving behavior and can safely transfer to different tasks and environments.
Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general, these problems entail non-convex estimation procedures, and, in practice, itera…
DFFL tackles federated learning with heterogeneous objectives and constraints.
problem Federated learning with clients having different objectives and feasible regions.
method Derived heterogeneity bounds for cost-vector distances and support-function/shape-distance terms. Lifted pointwise bounds to local-versus-federated excess-risk comparison.
result Federation is beneficial when the statistical advantage of pooling exceeds a client-specific heterogeneity penalty.
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.
Improved private learning of halfspaces with reduced sample complexity.
problem Private learning of halfspaces with reduced sample complexity.
method Iterative algorithm for solving linear feasibility problem, improving state-of-the-art results.
result Sample complexity reduced to d 2.5 ⋅ 2 log ∗ ∣ G ∣ d^{2.5} \cdot 2^{\log^*|G|} d 2.5 ⋅ 2 l o g ∗ ∣ G ∣ , improving d 2 d^2 d 2 factor. A multilevel optimization method for constrained problems.
problem Regularized constrained linear inverse problems with box constraints.
method Geometric multilevel optimization with varying discretization levels.
result Preserves feasibility of updates while speeding up computations.
New algorithms optimize actions under time-varying constraints without projecting.
problem Optimizing actions under time-varying constraints without projecting.
method Projection-free algorithms using linear optimization oracle.
result Guaranteed i l d e O ( T 3 / 4 ) ilde{O}(T^{3/4}) i l d e O ( T 3/4 ) regret and O ( T 7 / 8 ) O(T^{7/8}) O ( T 7/8 ) constraints violation. The paper classifies constraint mappings in optimization problems.
problem Understanding generic behavior of constraint functions in optimization.
method Using singularity theory of smooth mappings and subgroup classification.
result Families of constraint mappings are a residual set with at most 4 parameters.
Paper tackles SMPC for linear systems with unknown noise distribution.
problem Stochastic MPC for linear systems with chance state constraints and unknown noise distribution.
method Reformulate chance constraints, design robust benchmark SMPC, and develop adaptive SMPC with online noise statistics learning.
result Adaptive SMPC guarantees time-uniform satisfaction of unknown reformulated state constraints with high probability.
Unified framework for constrained diffusion models on nonconvex sets with efficient landing mechanism.
problem Efficiently modeling generative models under nonconvex constraints.
method Unified framework with overdamped and underdamped dynamics, landing mechanism.
result Significantly reduces computational cost while maintaining sample quality.