This work proposes ACTC for adaptive distributed learning under communication constraints.
problem Adaptive distributed learning in networks with communication constraints.
method ACTC (Adapt-Compress-Then-Combine) strategy with diffusion exchange of compressed updates.
result ACTC iterates converge to the optimizer with significant bit savings.
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic backward stochastic differential equation (BSDE in short). We characterize the op…
Paper studies how to combine regret minimizers for solving complex games.
problem Solving large-scale extensive-form games with constraints.
method Derives a calculus for constructing regret minimizers for composite convex sets.
result Local regret minimizers for simpler sets can be combined into an aggregate for composite sets.
The paper tackles MAP inference over non-convex constraints in safety-critical settings.
problem Efficiently computing MAP predictions subject to non-convex constraints is challenging.
method The paper investigates conditions for exact and efficient MAP inference over continuous variables and devises scalable algorithms for both tractable and general cases.
result The proposed methods outperform constraint-agnostic baselines and scale to complex densities.
Investigates optimal consumption and investment strategies with constraints in incomplete markets.
problem Optimal consumption and investment under constraints in incomplete markets.
method Characterizes optimal strategies via a quadratic BSDE, using martingale optimality criterion and Lyapunov functions.
result Obtains the verification theorem for optimal strategies in unbounded cases.
We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under…
Study optimal investment-reinsurance strategy for insurers under random coefficients and jumps.
problem Optimal investment-reinsurance strategy for insurers with random coefficients and jumps.
method Solves backward stochastic differential equations with jumps under a convex cone constraint.
result Optimal strategy and value remain the same even with random coefficients and jumps.
Study finds equivalence between MMV and MV preferences with conic constraints.
problem Monotone mean-variance portfolio selection under conic constraints.
method Closed-form solutions for optimal strategies under MMV and MV preferences.
result Optimal strategies coincide with and without the conic constraint.
Develops a method for near-optimal asset allocation with trading constraints.
problem Optimizing investment strategies in financial markets with trading constraints.
method Dual-control method using convex duality to generate bounds on optimal value function.
result Derives near-optimal asset allocation explicitly and demonstrates its accuracy in a real financial market.
Investor optimizes investment and consumption under uncertain market conditions with constraints.
problem Investor optimizes investment and consumption in a stochastic environment with model uncertainty and constraints.
method Robust control problem solved using stochastic Hamilton-Jacobi-Bellman-Isaacs equations, backward stochastic differential equations, and bounded mean oscillation martingale theory.
result Investor incurs utility loss when ignoring model uncertainty, and constraints impact optimal strategy and value function.
This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely studied in the literature and its terminal value, which dominates the claim of i…
Paper examines financial engineering problems and introduces AlphaZero for better replication strategies.
problem Replication portfolio construction in incomplete markets with non-convex constraints.
method Introduces AlphaZero-based system to compare with deep hedging method.
result AlphaZero outperforms deep hedging in non-convex environments, finding near-optimal strategies.
The paper proposes a control strategy for systems with sparse parameters using compressed sensing.
problem Control of linear systems with unknown sparse parameters under disturbances.
method Sparse estimation using Recursive Least Squares, improved with Basis Pursuit Denoising, and reformulated probabilistic constraints.
result The proposed algorithm outperforms existing methods in control design for systems with sparse impulse response parameters.
The paper optimizes investment strategies with constraints for life-cycle models.
problem Maximizing consumption, death benefit, and wealth under trading constraints.
method Deep pricing kernel approach to solve constrained portfolio optimization.
result Individuals reduce consumption, insurance demand, and wealth due to constraints.
Survey of Gaussian process constraints for modeling expensive data.
problem Modeling expensive data with physical constraints.
method Overview of various Gaussian process constraints and their implementation.
result Discussion of computational challenges introduced by constraints.
We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin; that is, it may be inadmissible fo…
In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to approximate the optimal strategy of a trader willing to unwind a large portfolio. The meth…
Optimizes trading strategy for cointegrated assets with bounded risk.
problem Maximizing profit from cointegrated assets with risk constraints.
method Formulates as convex optimization problem, then generalizes to bounded risk.
result Optimal strategy remains efficiently solvable even with bounded risk.
Investors face constraints in Heston's model; optimal allocation differs from naive capped strategy.
problem Optimizing portfolio allocation with convex constraints in Heston's stochastic volatility model.
method Applied duality methods to derive a closed-form solution.
result The optimal constrained portfolio allocation differs from the naive capped portfolio, leading to different wealth outcomes.
The paper applies thermodynamics to financial markets to prove no-arbitrage constraints.
problem No arbitrage in financial markets under price impact.
method Stochastic thermodynamics applied to financial trading cycles.
result Proves any round-trip trading strategy yields non-positive expected profit.
In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimalit…
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach is based on a general representation result for monotone convex functionals, a fu…
Study optimal asset allocation for insurers with multiple lines of business and constraints.
problem Maximize expected utility from dividends and wealth for insurers with multivariate insurance risk.
method Lagrangian convex duality techniques for continuous-time asset-allocation problem.
result Explicit characterization of optimal strategies under CRRA preferences.
Investment and consumption strategy optimized under uncertain conditions.
problem Optimal investment and consumption under logarithmic utility and uncertainty model.
method Characterized using quadratic BSDE.
result Optimal solution found.
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.
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading strategy in risky assets …
The paper solves stochastic control problems with implicit objectives, finding equilibrium strategies.
problem Stochastic control problems with implicitly defined objectives leading to time-inconsistency.
method Closed-loop equilibrium solutions in a controlled diffusion framework, providing sufficient and necessary conditions.
result Explicit characterization of equilibrium portfolio strategies in terms of ordinary differential equations.
The paper solves MMV and MV problems with random coefficients and finds shared optimal strategies.
problem Optimal trading strategies with random market coefficients.
method Backward stochastic differential equations (BSDEs) to find optimal strategies.
result MMV and MV problems share the same optimal portfolio and value under random coefficients.
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in a (possibly random and time-de…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few hundreds variables (in the underlying combinatorial problem). On the other hand…
In this paper, we consider the classical problem of utility maximization in a financial market allowing jumps. Assuming that the constraint set is a compact set, rather than a convex one, we use a dynamic method from which we derive a specific BSDE. We then aim at showing existence and uniqueness results for the introd…
Deep neural networks reduce portfolio tail-risk by 99% in crisis-era simulations.
problem Managing tail risk in financial portfolios.
method Parameterizing convex-risk minimization with deep neural networks.
result Significant reduction in one-day 99% CVaR.
Study asks if memory constraints affect optimal convex optimization methods.
problem Characterize the minimax number of queries for convex optimization with memory constraints.
method Analyze first order methods under memory limitations.
result Optimal oracle complexity may be achievable with limited memory.
Optimistic algorithm reduces regret and constraint violations in online convex optimization with adversarial constraints.
problem Online convex optimization with adversarial constraints.
method Improved algorithm using accurate predictions of loss and constraint functions.
result Improved bounds on regret and cumulative constraint violations.
Algorithm tackles constrained reinforcement learning with concave-convex and knapsack constraints.
problem Constrained episodic reinforcement learning with concave rewards and convex constraints.
method Modular analysis with strong theoretical guarantees for concave-convex and knapsack settings.
result Significantly outperforms existing approaches in constrained episodic environments.
Unified approach tackles logical constraints in mixed-integer optimization.
problem Logical constraints in mixed-integer optimization problems.
method Express logical constraints non-linearly, reformulate as convex binary optimization, solve using outer-approximation.
result Solves problems faster and at larger scale than existing methods.
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the ℓ1-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank a…
Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a d…
Paper solves high-order portfolio optimization with cardinality constraint.
problem Solving non-convex cardinality constrained high-order portfolio optimization.
method Transformed cardinality constraint into penalty term, proposed pDCA, pDCAe, and SCA algorithms.
result Proposed algorithms achieve high utility and sparse solutions efficiently.
Convex sparsity-promoting regularizations are ubiquitous in modern statistical learning. By construction, they yield solutions with few non-zero coefficients, which correspond to saturated constraints in the dual optimization formulation. Working set (WS) strategies are generic optimization techniques that consist in s…
New algorithm handles large-scale interaction models efficiently.
problem Large-scale interaction modeling with strong hierarchy constraints.
method Convex optimization, proximal gradient descent, screening rules, active-set strategy.
result Framework can handle p=50,000 with over 4900x speed-up. Improved COCO algorithms with better constraint control.
problem Achieving small regret and constraint violation in online convex optimization.
method Simple projection-based algorithm leveraging self-contraction geometry.
result Exponential improvement in cumulative constraint violation for strongly convex losses.
Paper optimizes DC pension fund management with VaR and relative performance constraints.
problem Optimizing DC pension fund performance under VaR and relative performance constraints.
method Introduced an auxiliary process to transform the problem into a self-financing problem, combined linearization, Lagrange dual, martingale, and concavification methods.
result Explicit investment strategies obtained for certain penalty and reward functions.
This work shows neural networks can solve non-convex constraints problems.
problem Training neural networks under non-convex constraints.
method Project stochastic gradient descent with no-regret analysis of online learning.
result Overparameterized neural networks achieve near-optimal and near-feasible solutions.
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.
Paper addresses distributed optimization with time-varying constraints.
problem Distributed online optimization with time-varying coupled inequality constraints.
method Proposes a distributed online primal-dual dynamic mirror descent algorithm.
result Achieves sublinear dynamic regret and constraint violation under natural stepsize sequences.
This paper considers online convex optimization (OCO) with stochastic constraints, which generalizes Zinkevich's OCO over a known simple fixed set by introducing multiple stochastic functional constraints that are i.i.d. generated at each round and are disclosed to the decision maker only after the decision is made. Th…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago…