This research tackles information design in multi-agent reinforcement learning.
problem Designing information to influence other adaptive agents in a non-stationary environment.
method Formulated Markov signaling game, introduced signaling gradient and extended obedience constraints.
result Developed efficient algorithm for mixed-motive tasks in multi-agent reinforcement learning.
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface Z in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-…
New algorithm for multi-player bandits with selfish players, achieving logarithmic regret.
problem Challenges of robustness to selfish players in multi-player bandits.
method First algorithm robust to selfish players achieving logarithmic regret, with or without collision observation.
result Achieved logarithmic regret for robust algorithms to selfish players in multi-player bandits.
Study contextual bandits with stage-wise constraints, proving regret bounds and extending results.
problem Contextual bandits with stage-wise constraints in high probability and expectation settings.
method Upper-confidence bound algorithms for linear and non-linear reward/cost functions, extending to multiple constraints.
result Regret bounds for various settings, including non-linear reward/cost functions.
In this note, we extend an evolutionary stochastic portfolio optimization framework to include probabilistic constraints. Both the stochastic programming-based modeling environment as well as the evolutionary optimization environment are ideally suited for an integration of various types of probabilistic constraints. W…
Reduces Lie (bi-)algebroids and Dirac manifolds using constraint vector bundles.
problem Reduction of Lie (bi-)algebroids and Dirac manifolds.
method Introduces constraint manifolds and constraint vector bundles; proves constraint Serre-Swan theorem; introduces Cartan calculus for constraint forms and multivector fields; shows compatibility with reduction.
result Reduction procedure for Lie (bi-)algebroids and Dirac manifolds.
Extends trading framework to incorporate real-world constraints.
problem Trading strategies in multi-player non-cooperative games with constraints.
method Re-framed as quadratic programming problem, constraints readily incorporated.
result Two-trader equilibria calculated dynamically.
Holistic GLMs add constraints for better model quality.
problem Improving classical linear regression models.
method Sparsity-inducing, sign-coherence, and linear constraints.
result Holistic GLMs reliably solve GLMs for various responses.
Simplifies neural network models by explicitly enforcing constraints in Cartesian coordinates.
problem Learning dynamics of complex systems efficiently and accurately.
method Embedding systems into Cartesian coordinates and using Lagrange multipliers to enforce constraints.
result Explicitly enforcing constraints leads to a 100x improvement in accuracy and data efficiency.
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…
This paper extends forecast reconciliation to non-linearly constrained time series.
problem Forecasting time series with non-linear constraints.
method Non-linearly Constrained Reconciliation (NLCR) algorithm that adjusts forecasts to meet non-linear constraints.
result NLCR significantly improves forecast accuracy compared to benchmarks.
The paper defines constraints for commuting endomorphisms in generalized tangent bundles.
problem Identifying constraints for commuting endomorphisms in generalized tangent bundles.
method Using Gröbner basis techniques to construct and study tensors forming ideals.
result Explicit construction and study of tensors forming ideals of commuting endomorphisms.
On a Lorentzian manifold the existence of a parallel null vector field implies certain constraint conditions on the induced Riemannian geometry of a space-like hypersurface. We will derive these constraint conditions and, conversely, show that every real analytic Riemannian manifold satisfying the constraint conditions…
We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the geometry of the center of mass of such solutions. We also review methods to con…
Investigates portfolio optimization with and without gearing constraints.
problem Improving portfolio weights for better alignment with expected returns.
method Extends the alpha-weight angle bound to include gearing constraints and uses theoretical arguments and simulations.
result Equally weighted portfolios are not preferable to mean-variance portfolios even with poor forecast ability and a badly conditioned covariance matrix.
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…
The paper extends utility maximization by integrating partial information and robust VaR constraints.
problem Optimal investment under partial information and robust VaR-type constraints.
method Combines partial information and robust regulatory constraints (VaR) to solve the utility maximization problem.
result Optimal wealth is a decreasing function of state price density, and depends on the overall evolution of the estimated market price of risk.
The study learns causal graphs from time series data using entropy measures.
problem Learning causal graphs from time series data.
method Constraint-based framework, information-theoretic measures, generalized causation entropy, PC and FCI algorithms.
result The methods effectively construct causal graphs from time series data.
Extended LPCMCI learns causal models from interventional data to minimize prediction error.
problem Optimizing prediction of target variables using causal models.
method Combining observational and interventional causal discovery methods.
result Extended LPCMCI allows 60.9% optimal prediction of target variables compared to 53.6% with original LPCMCI.
We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The c…
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.
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method used by Ise…
Study uses DRL with Lagrangian relaxation to solve temporal control tasks with STL constraints.
problem Optimal control problems with temporal logic constraints.
method Extended CMDP formulation, Lagrangian relaxation, two-phase constrained DRL algorithm.
result Demonstrated learning performance of the proposed algorithm through simulations.
We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds.
New algorithms reduce orthogonality constraint enforcement time in machine learning.
problem Efficiently solving orthogonality constraints in machine learning.
method Extending the landing algorithm to Stiefel manifold, incorporating stochastic and variance reduction techniques.
result All proposed methods achieve the same convergence rate as Riemannian counterparts enforcing constraints.
CANs improve GANs by enforcing structured constraints during training.
problem Generating valid structured objects like molecules and game maps from examples alone.
method Constrained Adversarial Networks (CANs) embed constraints into the model during training, penalizing invalid structures.
result CANs efficiently generate high-quality and novel valid structures.
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.
Let (gˉ,kˉ) be a solution to the maximal constraint equations of general relativity on the unit ball B1 of R3. We prove that if (gˉ,kˉ) is sufficiently close to the initial data for Minkowski space, then there exists an asymptotically flat solution (g,k) on R3 that ext…
New algorithm reduces regret and constraint violation in online convex optimization with predictions.
problem Online convex optimization with time-varying constraints and predictions.
method Primal-dual algorithm combining Follow-The-Regularized-Leader with adaptive steps.
result Achieves O(T43−β) regret and O(T21+β) constraint violation bounds. 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 ildeO(T3/4) regret and O(T7/8) constraints violation. Sharp dimension constraints for positive intermediate curvature metrics are established.
problem Proving sharp dimension constraints for metrics with positive intermediate curvature.
method Constructing counterexamples and extending rigidity results.
result Sharp dimension constraints for positive intermediate curvature metrics are established.
Extends graph factor system to quasi-median graphs.
problem Constraint relaxation for combinatorial HHS machinery.
method Relaxing domain constraints on combinatorial HHS machinery and extending factor system to quasi-median graphs.
result Factor system applied to quasi-median graphs.
Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.
problem Optimization problems involving rank-one convex functions with support constraints.
method Perspective reformulation techniques to exploit conic structure and establish convex hull results.
result Systematic perspective formulations for convex hull descriptions of sets with nonlinear separable or non-separable objective functions and combinatorial constraints.
Formula derived for Laplace-Beltrami on Stiefel manifold.
problem Finding Laplace-Beltrami operator on Stiefel manifold.
method Using the general framework of Laplace operators on constraint manifolds, derived the explicit formula in terms of ambient Euclidean coordinates.
result Extended previously known formulas for sphere and special orthogonal group.
Paper derives inequalities for eigenvalues of Witten-Laplacian under fixed volume constraint.
problem Eigenvalue inequalities of Witten-Laplacian on bounded domains.
method Rearrangement technique and trial functions under fixed weighted volume constraint.
result Several isoperimetric inequalities for eigenvalues of Witten-Laplacian.
In classification models fairness can be ensured by solving a constrained optimization problem. We focus on fairness constraints like Disparate Impact, Demographic Parity, and Equalized Odds, which are non-decomposable and non-convex. Researchers define convex surrogates of the constraints and then apply convex optimiz…
New single-loop algorithm tackles weakly convex constraints in stochastic optimization.
problem Optimization with weakly convex constraints in machine learning.
method Single-loop penalty-based stochastic algorithm using hinge-based penalty.
result Achieves state-of-the-art complexity for finding approximate KKT solutions.
In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch. It aims to lower the barrier for users wishing to use manifold constraints in deep learning applications, i.e., when the parameters are constrained to lie on a manifold. Such constraints include the popular orth…
We discuss multi-task online learning when a decision maker has to deal simultaneously with M tasks. The tasks are related, which is modeled by imposing that the M-tuple of actions taken by the decision maker needs to satisfy certain constraints. We give natural examples of such restrictions and then discuss a general …
Paper finds robust Λ-quantiles equal to extremal distributions.
problem Investigating robust models for Λ-quantiles with partial loss information. method Extending classical quantiles using Λ-quantiles and applying results from robust quantiles. result Robust Λ-quantiles equal to Λ-quantiles of extremal distributions. Study a continuous portfolio optimization with a new CVaR-like constraint using martingale approach.
problem Optimizing a portfolio under a new CVaR-like constraint that is not compatible with traditional methods.
method Follows a martingale approach in a complete market setting, solving a convex constrained minimization problem.
result Obtains a tractable and interpretable characterization of the optimal strategy.
We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abeli…
Optimizes multi-period portfolios with tail-risk constraints using neural networks.
problem Maximizing expected return while managing tail-risk constraints over multiple periods.
method Recurrent neural network approach to approximate optimal policy.
result Validated in financial and insurance models, capturing long-term risk dynamics.
In this paper, we investigate the common scenario where every candidate item for recommendation is characterized by a maximum capacity, i.e., number of seats in a Point-of-Interest (POI) or size of an item's inventory. Despite the prevalence of the task of recommending items under capacity constraints in a variety of s…
Extends Dirac structures to infinite dimensions for mechanical systems.
problem Adapting finite-dimensional Dirac structures to infinite-dimensional settings.
method Introduces partial Dirac structures and applies variational techniques to constraint Lagrangians on subbundles and singular distributions.
result Characterizes normal geodesics for conical Finsler metrics on Banach manifolds.
New algorithm for contextual bandits with linear constraints using regression.
problem Contextual bandits with packing and covering constraints.
method Modular Lagrangian approach via regression.
result First vanishing-regret guarantees for CBwLC (or CBwK).
Paper extends LME models to allow sign constraints on coefficients with SDTN random effects.
problem Inference with sign constraints on random effects in LME models.
method Proposes SDTN distribution for random effects and develops likelihood-based approaches for estimation.
result Proposed constrained model improves real-world interpretations and achieves satisfactory performance.
In this paper, we study a new type of BSDE, where the distribution of the Y-component of the solution is required to satisfy an additional constraint, written in terms of the expectation of a loss function. This constraint is imposed at any deterministic time t and is typically weaker than the classical pointwise one a…