The study examines higher-order modern portfolio theory with complex critical points and feasible portfolio variety.
problem Understanding the complex critical points and feasible portfolio variety in higher-order modern portfolio theory.
method Established genericity conditions for utility functions with higher-order cumulants, analyzed discriminant loci, and determined the dimension and degree of the feasible portfolio variety.
result The utility function has a constant number of complex critical points under genericity conditions, and the feasible portfolio variety has a determined dimension and degree.
We describe computationally efficient methods for learning mixtures in which each component is a directed acyclic graphical model (mixtures of DAGs or MDAGs). We argue that simple search-and-score algorithms are infeasible for a variety of problems, and introduce a feasible approach in which parameter and structure sea…
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.
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.
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.
Optimizes neural network training by dynamically updating Tucker decomposition ranks.
problem Redundant parameters in neural network architectures.
method Geometry-aware training of factorized layers in tensor Tucker format.
result Optimal locally approximating the original dynamics without initial rank knowledge.
The deep learning trend has recently impacted a variety of fields, including communication systems, where various approaches have explored the application of neural networks in place of traditional designs. Neural networks flexibly allow for data/simulation-driven optimization, but are often employed as black boxes det…
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.
USAC balances pessimism and optimism in actor-critic training for better exploration and performance.
problem Excessive pessimism limits exploration, while excessive optimism leads to high-risk behaviors.
method Utility Soft Actor-Critic (USAC) dynamically adapts exploration based on critic uncertainty.
result USAC consistently outperforms state-of-the-art algorithms in continuous control tasks.
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.
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this paper, we explore an optimistic, or best-case view of uncertainty and show that it …
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…
Enhances OTA FL algorithms by defining inverse feasibility for linear models.
problem Improving security and privacy in over-the-air federated learning.
method Defines inverse feasibility as an upper bound on condition number, analyzes existing model, proposes new model.
result Proposes a new OTA FL model with enhanced characteristics.
Convex learning for diverse invariances in semi-inner-product space.
problem Efficiently learning invariant representations for a wide range of invariances.
method Developed a convex representation learning algorithm for generalized invariances modeled as semi-norms, introducing Euclidean embeddings for kernel representers in a semi-inner-product space.
result Accurate invariant representations learned efficiently and effectively, validated by experiments.
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…
New algorithm exploits curvature of feasible sets for fast online convex optimization.
problem Online convex optimization with fast rates.
method Adapting FTL algorithm to curvature of feasible sets.
result Achieves logarithmic regret bound of O(ρlogT) in stochastic environments. Robots hold promise in many scenarios involving outdoor use, such as search-and-rescue, wildlife management, and collecting data to improve environment, climate, and weather forecasting. However, autonomous navigation of outdoor trails remains a challenging problem. Recent work has sought to address this issue using de…
Variational Inference shows promise for Bayesian GARCH model estimation.
problem Bayesian estimation of GARCH-family models using Monte Carlo sampling.
method Variational Inference as an alternative to Monte Carlo sampling.
result Variational Inference is a reliable and competitive method for Bayesian learning in GARCH-like models.
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.
Many real-world applications require robust algorithms to learn point processes based on a type of incomplete data --- the so-called short doubly-censored (SDC) event sequences. We study this critical problem of quantitative asynchronous event sequence analysis under the framework of Hawkes processes by leveraging the …
The paper studies SDP feasibility and sos ranks for specific polynomials.
problem Characterizing sos representations of nonnegative polynomials.
method Explicit SDP formulation based on Clifford systems.
result Quantitative rank bounds for sos representations, with rigidity.
High-dimensional random geometry shows phase transitions in various problems.
problem Phase transitions in high-dimensional random geometry.
method Analysis of various financial, optimization, and ecological problems.
result Links between seemingly distant fields and further ramifications.
In this study, we focus on the market clearing problem of Turkish day-ahead electricity market. We propose a mathematical model by extending the variety of bid types for different price regions. The commercial solvers may not find any feasible solution for the proposed problem in some instances within the given time li…
Paper addresses quadratic feasibility problems and their sample complexity.
problem Recovering complex vectors from quadratic measurements.
method Analyzes conditions for identifiability and explores optimization landscape.
result Gradient algorithms can converge to globally optimal solutions with high probability.
New algorithm improves convergence for non-convex problems with boundaries.
problem Optimizing non-convex problems with constraints.
method Reflected Gradient Langevin Dynamics with probabilistic representation.
result Promising convergence rates, faster than existing methods.
Smartphones can estimate heart rate from other sensor data.
problem Gaps in heart rate data from wearable sensors.
method Regression, SVM, and random forest algorithms to estimate heart rate from smartphone data.
result Smartphone data can improve heart rate estimation from wearable sensors.
Bayesian framework proves thresholds for multi-graph alignment feasibility.
problem Determining when multi-graph alignment is statistically possible.
method Developed a Bayesian estimation framework over metric spaces.
result Identified thresholds for Gaussian and sparse Erdős-Rényi models.
Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solvi…
Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at every iteration. Here we present Firefly Monte Carlo (FlyMC) an auxiliary variabl…
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.
A fundamental task in machine learning and related fields is to perform inference on Bayesian networks. Since exact inference takes exponential time in general, a variety of approximate methods are used. Gibbs sampling is one of the most accurate approaches and provides unbiased samples from the posterior but it has hi…
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.
The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion entropy analysis (DEA) to …
Detecting correlated trees helps align sparse graphs.
problem Detecting correlation between trees for sparse random graphs.
method MPAlign message-passing algorithm for graph alignment.
result MPAlign succeeds in polynomial time for partial alignment.
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 \( \widetilde{O}(d^2/Γ^2) \).
Paper defines conditions for feasible correlation matrices from factor structures.
problem Feasibility of option implied correlation matrices in non-FX markets.
method Quantitative and economic approaches to solve the nearest correlation matrix problem.
result Introduces methods to ensure feasible correlation matrices from factor structures.
Mathematical framework for transfer learning feasibility and transfer risk.
problem Theoretical analysis of transfer learning.
method Reformulated transfer learning as an optimization problem, introduced transfer risk concept.
result Demonstrated the potential and benefits of incorporating transfer risk in transfer learning evaluation.
Sharpe et al. proposed the idea of having an expected utility maximizer choose a probability distribution for future wealth as an input to her investment problem instead of a utility function. They developed a computer program, called The Distribution Builder, as one way to elicit such a distribution. In a single-perio…
Paper shows Burer-Monteiro method can solve SDPs in polynomial time under smoothed analysis.
problem Solving large-scale semidefinite programs (SDPs) efficiently.
method Perturbing SDP to create a nonconvex program in Y where Y is an nimesp matrix. result The Burer-Monteiro method can solve SDPs to any desired accuracy in polynomial time under certain conditions.
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.
Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being maximized. Unfortunately, in many realistic settings F is too expensive to evaluat…
Having the right assortment of shipping boxes in the fulfillment warehouse to pack and ship customer's online orders is an indispensable and integral part of nowadays eCommerce business, as it will not only help maintain a profitable business but also create great experiences for customers. However, it is an extremely …
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…
To overcome the curse of dimensionality and curse of modeling in Dynamic Programming (DP) methods for solving classical Markov Decision Process (MDP) problems, Reinforcement Learning (RL) algorithms are popular. In this paper, we consider an infinite-horizon average reward MDP problem and prove the optimality of the th…
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…
SCBO tackles constrained optimization in high dimensions.
problem Optimizing complex, high-dimensional functions with constraints.
method Proposes scalable constrained Bayesian optimization algorithm.
result Demonstrates excellent performance on various benchmarks.
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.
PrivacyFL simulates privacy-preserving federated learning.
problem Ensuring privacy in federated learning environments.
method Extensible, configurable simulator for federated learning.
result PrivacyFL checks feasibility and improves model accuracy.