This paper shows how to hedge financial risks with integer investments.
problem Evaluating the minimal super-hedging price with integer-valued strategies for arbitrary payoffs.
method Formulated a dynamic programming principle to evaluate the minimal super-hedging price with integer-valued strategies for continuous piecewise affine terminal claims.
result It is possible to evaluate the minimal super-hedging price with integer-valued strategies for discrete-time, arbitrary Ω.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
Paper develops machine learning algorithms to learn optimal integer weights for clinical risk scores.
problem Deriving optimal integer weights for clinical risk scores without computational burden.
method Flexible greedy optimization strategy to directly optimize a value function.
result Constructed an integer-weighted comorbidity score for measuring post-discharge mortality risk.
Paper uses RL to optimize branching strategy in B&B algorithms.
problem Optimizing Branch and Bound algorithms for mixed integer linear programs.
method FMSTS, a Reinforcement Learning approach for variable selection.
result FMSTS outperforms commercial solvers in efficiency and generalization.
Paper proposes algorithms for BMF using integer programming.
problem Approximating binary input matrix as product of two smaller binary factors.
method Alternating optimization strategy using integer programming to solve subproblems and combine solutions.
result Proposed algorithms outperform state of the art on medium-scale problems.
Paper optimizes battery storage in multiple energy markets for better profits.
problem Optimizing battery storage participation in multiple energy markets to balance supply and demand.
method Developed a joint bidding strategy combining intraday and frequency markets using mixed integer linear programming and a learned classifier strategy.
result The LCS increases overall profits by over 4% compared to static strategies and by more than 3% over a naive dynamic benchmark.
New LNS framework improves integer program solving.
problem Solving large-scale integer linear programs efficiently.
method Large neighborhood search with imitation and reinforcement learning.
result Framework significantly outperforms commercial solvers.
MEC-IP uses IP to efficiently find MECs in BNs from observational data.
problem Discovering Markov Equivalent Classes (MECs) in Bayesian Networks (BNs) efficiently.
method Clique-focusing strategy and EMSG for MEC discovery via Integer Programming.
result Significant reduction in computational time and improved accuracy.
Optimizes marketing strategies with practical constraints.
problem Adjusting marketing activities with minimum and maximum changes.
method Formulated as a mixed integer nonlinear program (MINLP), reformulated for computational efficiency.
result Significant improvements in solution process for realistic problems.
New method optimizes mixed integer optimization for hierarchical modeling of clustered and longitudinal data.
problem Optimizing subset selection in hierarchical models with clustered and longitudinal data.
method Distribution-free mixed-integer optimization approach for cluster-aware regression.
result The method efficiently solves problems within minutes and outperforms traditional models in generating sparse solutions with high predictive power.
Mixed-integer optimization improves fairness and transparency in machine learning models.
problem Ensuring fairness and transparency in machine learning models deployed in sensitive areas.
method Embedding responsible ML considerations directly into the learning process using mixed-integer optimization.
result MIO enables the learning of inherently transparent models that can incorporate fairness or other constraints.
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning proble…
We study the problem of allocating stocks to dark pools. We propose and analyze an optimal approach for allocations, if continuous-valued allocations are allowed. We also propose a modification for the case when only integer-valued allocations are possible. We extend the previous work on this problem to adversarial sce…
This paper recovers smooth functions from noisy modulo samples using a three-stage strategy.
problem Recovering Hölder smooth functions from noisy modulo samples.
method Three-stage strategy: denoising with local polynomial estimators, unwrapping, and spline-based quasi-interpolant.
result Uniform error rates for Hölder class functions with high probability.
New method improves portfolio selection by filtering noisy covariance matrices.
problem Noisy covariance matrices in financial datasets affect portfolio performance evaluation.
method Combinatorial Optimization approach using Mixed Integer Quadratic Programming.
result Our method outperforms existing filtering strategies for real financial datasets.
In this paper, we present a novel approach to construct multiclass classifiers by means of arrangements of hyperplanes. We propose different mixed integer (linear and non linear) programming formulations for the problem using extensions of widely used measures for misclassifying observations where the \textit{kernel tr…
We present a novel optimization strategy for training neural networks which we call "BitNet". The parameters of neural networks are usually unconstrained and have a dynamic range dispersed over all real values. Our key idea is to limit the expressive power of the network by dynamically controlling the range and set of …
New q-deformed integers help compute Jones polynomials efficiently.
problem Computing Jones polynomials of rational links efficiently.
method Defining q-deformed integers from pairs of coprime integers and using them to compute Jones polynomials.
result Efficient algorithm for computing Jones polynomials of rational links.
This paper tackles energy-efficient machine learning on low-power devices.
problem Energy consumption in machine learning due to data communication.
method Dynamic averaging for integer exponential families on low-power processors.
result Achieves comparable model quality with significantly less communication and energy.
CPP solves chance constrained optimization problems with a framework that combines samples and quantile lemma.
problem Chance constrained optimization problems with constraints on random variables.
method CPP framework using samples and quantile lemma to transform into deterministic problem.
result CPP provides a posteriori guarantees on constraint satisfaction and can handle different types of chance constraints.
Generalized Steinberg module presentation for Gaussian and Eisenstein integers.
problem Presenting Steinberg modules for specific number rings.
method Generalization of Bykovskii's presentation to Gaussian and Eisenstein integers.
result Generalization does not yield a presentation for all Euclidean number rings.
We present a new proof of Thurston's theorem that the unit ball of a seminorm on Rd taking integer values on Zd is a polyhedra defined by finitely many inequalities with integer coefficients.
Surgery obstructions extended to integer homology spheres using Heegaard Floer homology.
problem Obstructing knots in integer homology spheres using surgery.
method Extending Heegaard Floer homology obstructions to all integer homology spheres for both positive and negative surgeries.
result Deduced a lower bound on b2(W) for smooth cobordism between integer homology spheres. New model uses Half-Full/Half-Empty approach for better portfolio selection.
problem Improving portfolio selection through behavioral finance.
method Generalized Half-Full/Half-Empty approach to positive/negative lotteries, developing nonconvex optimization and mixed-integer linear programming models.
result The Half-Full/Half-Empty model outperforms other methods in risk and profitability.
IDF++ improves integer discrete flows for lossless compression.
problem Theoretical limitations of integer discrete flows for lossless compression.
method Investigated and improved integer discrete flows, addressing gradient bias and architecture modifications.
result Different architecture modifications improve integer discrete flows for lossless compression.
A new framework for predictive clustering and optimization.
problem Finding clusters of data that yield low error on a supervised target.
method Generalized optimization framework using MILP and MM for scalability.
result Models can uncover different interpretable discrete cluster structures.
New links split by integer homology spheres but not by others.
problem Characterizing links split by integer homology spheres.
method Constructing specific links and homology spheres.
result Infinite families of links and homology spheres split by specific ones but not by others.
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
problem Optimizing functions with mixed variable types (continuous, integer, categorical).
method Merges MCTS for categorical and GP for continuous variables, integrates UCTS search strategy, and dynamically selects kernels.
result Hybrid models outperform traditional methods in Bayesian optimization.
A new portfolio model considers investor aversion to loss and risk.
problem Constructing a robust portfolio under uncertain asset returns and investor aversion.
method Distributional robust optimization (DRP) with a Wasserstein ball centered on empirical distribution, mixed-integer quadratic programming, and hybrid algorithm.
result Empirical testing shows superior performance in asset allocation compared to common strategies.
We use Nathanson's g-adic representation of integers to relate metric properties of Cayley graphs of the integers with respect to various infinite generating sets S to problems in additive number theory. If S consists of all powers of a fixed integer g, we find explicit formulas for the smallest positive intege…
Geometric proof shows primes of form 3k+1 are norms of Eisenstein integers.
problem Geometric proof of primes of form 3k+1 being norms of Eisenstein integers.
method Geometric proof using Penner's λ-length and norms of Eisenstein integers.
result Every prime p of the form 3k+1 is the norm of an Eisenstein integer. ODTLearn learns optimal decision trees for predictive and prescriptive tasks.
problem Learning optimal decision trees for high-stakes predictive and prescriptive tasks.
method Mixed-integer optimization framework and object-oriented design.
result Implementation of optimal decision trees for various tasks.
New method for probabilistic modeling of integer submodular functions.
problem Lack of probabilistic modeling for integer submodular functions.
method Proposed Generalized Multilinear Extension and block-coordinate ascent algorithm.
result Demonstrated effectiveness and viability on real-world datasets.
An elementary proof shows that quasi-isometric groups to integers are virtually integers.
problem Proving that quasi-isometric groups to integers are virtually integers.
method An elementary proof approach.
result Any finitely generated group quasi-isometric to the integers is virtually the integers.
Study area-minimizing subgraphs in integer lattices.
problem Finding the most efficient subgraphs in integer lattices.
method Formulated functions of bounded variations, classified subgraphs in 2D, proved properties in higher dimensions.
result Classified area-minimizing subgraphs in 2D integer lattice up to isomorphisms.
New method finds lattice polygons that can be dissected into triangles with integer areas.
problem Finding lattice polygons that can be dissected into triangles with integer areas.
method A new version of Sperner's Lemma.
result Simple and complete description of lattice polygons that can be dissected into triangles with integer areas.
Neural networks with integer weights approximate continuous functions efficiently.
problem Approximating continuous functions using neural networks with integer weights.
method Integrates superexpressive activation functions and integer weights.
result Convergence rate of order n2β+d−2βlog2n for neural network regression. High-frequency trading strategy boosts battery storage profits.
problem Maximizing revenue for battery energy storage systems in intraday markets.
method Adapted dynamic programming for continuous intraday markets, considering limit order book dynamics.
result Dynamic programming strategy outperforms standard re-optimization methods, increasing profits by 58% and 14% respectively.
New examples show non-integer Hausdorff dimensions in collapsing spaces.
problem Understanding Hausdorff dimensions in collapsing Ricci limit spaces.
method Provided examples of spaces with irregular Hausdorff dimensions.
result Hausdorff dimension of singular set exceeds regular set's dimension.
The integer hull of a polyhedron is the convex hull of the integer points contained in it. We show that the vertices of the integer hulls of a rational family of polyhedra of size O(n) have quasipolynomial coordinates. As a corollary, we show that the stable commutator length of elements in a surgery family is a ratio …
Paper uses integer programming for non-convex boosting in classification.
problem Improving classification performance using non-convex optimization.
method Non-convex boosting via integer programming.
result Results comparable to or better than state-of-the-art.
We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeli…
A new combinatorial approach groups regression coefficients for improved accuracy.
problem Grouping regression coefficients to reveal shared values within groups.
method Introduces L0-Fusion, a combinatorial grouping approach using mixed integer optimization. result L0-Fusion achieves grouping consistency under weak grouping sensitivity conditions. The article calculates a multiplying factor to convert rational Vassiliev invariants to integer-valued ones.
problem Converting rational valued Vassiliev invariants to integer-valued ones.
method Calculates the minimal multiplying factor λ needed for rational Vassiliev invariants to become integer-valued.
result Obtains a set of integer-valued Vassiliev invariants.
Improved RTM uses integer weights to reduce computation and increase interpretability.
problem Lack of interpretability in nonlinear regression models.
method Integer weighted RTM clauses, combined with a novel learning scheme.
result Significantly reduced computation cost with improved accuracy.
New symplectic embedding obstructions found for polydisks into half-integer ellipsoids.
problem Obstructing symplectic embeddings of polydisks into half-integer ellipsoids.
method Combinatorial criterion developed by Hutchings to obstruct symplectic embeddings.
result Optimal inclusion conditions for symplectic embeddings of polydisks into half-integer ellipsoids.
The article describes Horn(p,q) with integer p and q.
problem Classical Horn's conjecture for Horn(p,q).
method Recursive description of Horn(p,q).
result Obtained a recursive description of Horn(p,q).
Infinite knots have non-integer trace values.
problem Finding knots with non-integer trace values.
method Proved existence of infinitely many non-homeomorphic hyperbolic knot complements with specific trace properties.
result Infinitely many non-homeomorphic hyperbolic knot complements with non-integer trace values.