Study shows equivalence of four risk constraints in non-concave optimization problems.
problem Investigating risk constraints in non-concave optimization for financial companies.
method Analytical solutions for four risk constraints (ES, EDS, VaR, AVaR) under non-concave optimization.
result All four risk constraints lead to the same optimal solution, differing from concave optimization.
Optimizes algorithms for non-concave bandit problems.
problem Optimizing algorithms for non-concave bandit problems.
method Unified zeroth-order optimization paradigm.
result Minimax-optimal algorithms in the dimension for low-rank generalized linear bandit problems.
Optimizes investment under uncertain time horizons with non-concave utility.
problem Optimizing investment decisions with non-concave utility and uncertain time horizons.
method Established necessary and sufficient conditions for optimality, suggested recursive procedure for non-concave utility.
result Optimal investment strategies under uncertain time horizons exhibit multimodal distribution, indicating flexibility in switching between local maximizers.
The paper analyzes portfolio selection with non-concave utility and transaction costs.
problem Non-concave utility maximization with proportional transaction costs.
method Two-step procedure: asymptotic terminal behavior analysis and discontinuous viscosity solution.
result Optimal portfolio strategies can differ significantly from the frictionless case due to transaction costs.
We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the no-arbitrage condition characterization and the existence of an optimal portfolio i…
This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the standard setting, a possibly non-concave utility function U is considered, with domain of definition R. Simple conditio…
We solve S-shaped utility portfolio selection with SD constraints using algorithms and neural networks.
problem Optimizing portfolios with S-shaped utility functions under SD constraints.
method First-order SD constraint solution, numerical algorithm for SSD, neural network approach.
result Effective numerical and neural network solutions for SSD constrained problems.
Paper analyzes adversarial dynamics in neural networks.
problem Vulnerability of neural networks to adversarial perturbations.
method Analyzed the dynamics of maximization step in adversarial training.
result Projected gradient ascent finds a local maximum in polynomial iterations.
PAPAL algorithm finds mixed Nash equilibria in continuous games.
problem Finding mixed Nash equilibria in non-convex, non-concave games.
method Particle-based Primal-Dual Algorithm (PAPAL) for weakly entropy-regularized min-max optimization.
result PAPAL offers non-asymptotic convergence guarantees for ε-mixed Nash equilibrium. The paper analyzes how optimization algorithms affect the generalization of minimax models.
problem The generalization performance of minimax models trained with different optimization algorithms.
method Analysis of gradient descent ascent (GDA) and proximal point method (PPM) algorithms under convex concave and non-convex non-concave settings.
result The PPM algorithm ensures a bounded excess risk in convex concave problems, while GDA's generalization depends on solving subproblems simultaneously.
We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…
Study optimal control strategy for hedge funds managers with PSAHARA utility family.
problem Optimizing risk and reward in incomplete markets with non-monotone risk aversion and convex compensation.
method Introduced PSAHARA utility family to model non-monotone risk aversion and convex compensation. Proved concavification techniques for non-concave utility functions. Derived explicit optimal control strategy.
result PSAHARA utility induces risk-taking behavior even with convex compensation, leading to high returns and volatility.
The Piyavskii-Shubert algorithm is analyzed for global optimization of Lipschitz functions.
problem Maximizing a non-concave Lipschitz function over a compact domain.
method Sequential function evaluations using a bandit-optimization approach.
result New bounds on the number of evaluations needed for optimization accuracy.
Framework for robust control under model uncertainty, improving financial derivatives hedging.
problem Model uncertainty in financial derivatives hedging.
method Dynamic programming principle for solving one-step optimization problems.
result Robust hedging strategy outperforms model-based strategies during adverse scenarios.
This paper studies the optimal risk-averse timing to sell a risky asset. The investor's risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price -- the geometric Brownian motion and exponential Ornstein-Uhlenbeck models -- to account for, respectiv…
A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the concavity of the speed as a function of principal curvatures.
Paper improves adversarial training using a learned optimizer.
problem Improving robustness of deep learning models against adversarial attacks.
method Empirically identified PGD attack's limitations and used a learning-to-learn framework to train an adaptive inner optimizer.
result The proposed framework consistently improves model robustness over traditional adversarial training methods.
Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.
problem Understanding dynamics of zero-sum games with hidden structure.
method Gradient Descent Ascent applied to hidden zero-sum games with specific convex-concave structure.
result Gradient Descent Ascent converges to von-Neumann solution in strictly convex-concave hidden games.
The paper examines how background risk affects portfolio selection and optimal reinsurance design.
problem Maximizing the probability of reaching a financial goal in the presence of background risk.
method Quantile formulation method to derive optimal solutions explicitly.
result The presence of background risk does not change the solution shape but alters the parameter values.
Study optimal reinsurance contracts to prevent moral hazard under non-concave premium principles.
problem Preventing moral hazard in reinsurance contracts under non-concave premium principles.
method Develops optimal reinsurance contracts under a diffusion risk model with incentive compatibility constraints and extended distortion premium principles.
result An optimal reinsurance contract exists and is characterized by solving a double obstacle problem.
The paper solves an insurance problem using mean-variance and rank-dependent utility theory.
problem Formulating and solving an insurance problem with rank-dependent utility and mean-variance premium principle.
method Formulated as a non-concave maximization problem, then turned into a concave quantile optimization problem, solved using calculus of variations.
result An optimal insurance contract is derived and numerically computed.
New framework for ranking distributions using variable fractional parameters.
problem Ordering distributions with varying steepness and local non-concavities.
method Introducing a function γ:Ro[0,1] to replace the fixed parameter in fractional SD. result Enables ranking of a broader range of distributions and incorporates dynamic greediness.
FPCA optimizes fairness in target vectors' span.
problem Fairness in principal component analysis for multiple target vectors.
method Non-concave maximization of worst projected target norm using sub-gradient descent.
result Optimization landscape is benign with globally optimal local minima.
In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global objective function and nodes are allowed to exchange information only with their n…
Unified formula for optimal portfolio under piecewise hyperbolic risk aversion.
problem Optimizing portfolios with piecewise hyperbolic risk aversion utilities.
method Derive a unified closed-form formula for the optimal portfolio.
result Unified formula reflects risk aversion behaviors and risk-taking behaviors.
Study on optimal fees in hedge funds with first-loss compensation.
problem Determining the best fee structure for hedge funds with first-loss compensation.
method Solved the manager's non-concave utility maximization problem, calculated Pareto optimal first-loss schemes, and maximized a decision criterion on this set.
result Traditional fees are not Pareto optimal, and the preferred first-loss coverage guarantee varies with investor and market factors.
Investigates portfolio selection with transaction costs and stochastic volatility, using deep learning for computation.
problem Optimal portfolio selection with transaction costs and stochastic volatility.
method Two-factor stochastic volatility model, option-implied utility function, deep learning policy iteration.
result Deep learning method effectively computes optimal investment decisions under transaction costs and stochastic volatility.
In recent years, Generative Adversarial Networks (GANs) have drawn a lot of attentions for learning the underlying distribution of data in various applications. Despite their wide applicability, training GANs is notoriously difficult. This difficulty is due to the min-max nature of the resulting optimization problem an…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe algorithm that has access to the full gradient of the objective functions. We show t…
Novel framework for portfolio selection considering utility and risk.
problem Maximizing utility subject to risk constraints with various utility and risk functionals.
method General framework accommodating non-concave utilities and non-convex risk measures. Characterization of well-posedness using a simple either-or criterion.
result Minimal condition for well-posedness: either utility or risk must be sensitive to large losses.
This paper investigates Pareto optimal (PO, for short) insurance contracts in a behavioral finance framework, in which the insured evaluates contracts by the rank-dependent utility (RDU) theory and the insurer by the expected value premium principle. The incentive compatibility constraint is taken into account, so the …
Develops deep learning methods for solving S-shaped utility maximisation problems.
problem Optimizing portfolios with S-shaped utility and random benchmarks.
method Uses deep learning and duality methods to solve the Hamilton-Jacobi-Bellman equation and adjoint equation.
result Demonstrates the accuracy of deep learning methods for non-concave utility maximisation problems.
Gaussian random fields are a powerful tool for modeling environmental processes. For high dimensional samples, classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as the evaluation of the Cholesky factorization or solving linear systems. Recently, Anit…
Survey of advances in non-convex min-max optimization for applications.
problem Finding optimal solutions in non-convex, non-concave min-max problems.
method Selective review of theoretical and algorithmic advances.
result Exciting recent advances in solving non-convex min-max problems.
In order to identify important variables that are involved in making optimal treatment decision, Lu et al. (2013) proposed a penalized least squared regression framework for a fixed number of predictors, which is robust against the misspecification of the conditional mean model. Two problems arise: (i) in a world of ex…
Wasserstein GANs are shown to have hidden convexity, enabling exact solutions with convex optimization.
problem Non-convex and non-concave optimization in GANs.
method Convex duality analysis of Wasserstein GANs with two-layer neural network discriminators.
result Wasserstein GANs can be solved exactly with convex optimization under certain conditions.
New method improves convergence for smooth games.
problem Improving convergence for smooth games.
method Stochastic Hamiltonian Gradient Methods (SHGD).
result SHGD converges linearly to the neighbourhood of a stationary point.
This thesis explores how submodularity aids in optimizing non-convex functions and validating algorithms.
problem Understanding which functions can be optimized efficiently in non-convex settings.
method Introducing continuous submodularity and developing algorithms for maximizing these functions.
result Characterization and optimization of continuous submodular functions with strong guarantees.
Develops a new parabolic equation for surfaces, proving long-time existence and convergence.
problem Extending elliptic equations to parabolic settings for surfaces.
method Introduces a parabolic analogue of the elliptic split-type Monge-Ampère equation.
result Proves long-time existence and convergence conditions for the new equation.
New study shows min-max algorithms can converge to non-stationary points.
problem Challenges in min-max optimization due to periodic cycles and spurious attractors.
method Analyzed state-of-the-art algorithms and heuristics in non-convex/non-concave problems.
result Spurious attractors can prevent min-max algorithms from reaching true optima.
New methods tackle complex inverse problems with scalable optimization-based MCMC.
problem Estimating high-dimensional model parameters and hyperparameters in nonlinear hierarchical statistical inverse problems.
method Optimization-based Markov chain Monte Carlo (MCMC) methods using RTO and pseudo-marginal MCMC.
result Efficient sampling tools for hierarchical Bayesian inversion with robust performance to model parameter dimensions.
The paper explains how simple methods can converge to optimal solutions in complex neural games.
problem Finding optimal solutions in neural games with non-convex objectives.
method Theoretical framework using hidden convexity and overparameterization, with path-length bounds and PŁ conditions.
result Simple gradient methods can converge to Nash equilibria in non-convex min-max games under certain conditions.
FedIV uses federated GMM for IV analysis in non-i.i.d. data.
problem Efficient IV analysis in non-i.i.d. federated data.
method Federated GMM via FedGDA algorithm.
result Federated solution consistently estimates local moment conditions.
The paper studies continuous submodular functions and their optimization.
problem Maximizing continuous submodular functions in poly. time.
method Characterization of continuous submodularity, operations preserving it, and algorithms for constrained maximization.
result Continuous submodularity is equivalent to a weak DR property, leading to continuous DR-submodular functions with the full DR property.
This paper studies a Value-at-Risk (VaR)-regulated optimal portfolio problem of the equity holders of a participating life insurance contract. In a setting with unhedgeable mortality risk and complete financial market, the optimal solution is given explicitly for contracts with mortality risk using a martingale approac…
Adam-type optimizers show one-sided convergence in GAN training, not reaching critical points.
problem Theoretical understanding of Adam-type optimizers in non-convex non-concave min-max optimization.
method Empirical and theoretical analysis of Adam-type algorithms' convergence in GAN training.
result Adam-type algorithms converge to one-sided first order stationary points under the one-sided MVI condition.
In this paper, we first investigate the flow of convex surfaces in the space form R3(κ) (κ=0,1,−1) expanding by F−α, where F is a smooth, symmetric, increasing and homogeneous of degree one function of the principal curvatures of the surfaces and the power α∈(0,1] for κ=0,−1 and α=1 for κ=1…