Hamiltonian dynamics-based algorithms achieve deterministic and accelerated convergence for convex optimization.
problem Accelerating convex optimization
method Hamiltonian dynamics
result Hamiltonian dynamics-based algorithms achieve deterministic and accelerated convergence for convex optimization.
Extends optimal transport to dynamic and martingale settings.
problem Dynamic and martingale relaxation of optimal transport problems.
method Extends Benamou-Brenier formula to weak optimal transport and introduces barycentric optimal transport.
result Relates barycentric optimal transport to martingale Benamou-Brenier formula.
TrajectoryNet models dynamic cellular trajectories using optimal transport.
problem Modeling continuous and non-linear paths in dynamic processes.
method Continuous normalizing flows linked to dynamic optimal transport.
result TrajectoryNet improves interpolation of cellular distributions.
Proposes methods for learning optimal dynamic treatment regimes robust to unconfoundedness violations.
problem Estimating optimal dynamic treatment regimes using historical observational data when unconfoundedness is violated.
method Utilizes proximal causal inference framework to propose three nonparametric identification methods, a (K+1)-robust method, and establish a semiparametric efficiency bound.
result Establishes the (K+1)-robust method for learning optimal dynamic treatment regimes, validating its efficiency and multiple robustness through numerical experiments.
Paper introduces dynamic strategies for multi-period investment models.
problem Optimizing investment strategies over multiple periods with risk and return considerations.
method Developed a Bellman principle for discrete time multi-period mean-variance models, leading to dynamic optimal strategies and efficient frontiers.
result Dynamic optimal strategies can achieve higher returns with lower risk compared to the 1/n strategy.
Universal online optimization for dynamic environments using uniclass prediction.
problem Online optimization in changing environments with dynamic regret.
method Reduces dynamic online optimization to uniclass prediction problem, allowing control over dynamic regret bounds.
result First paper with state-of-the-art dynamic regret guarantees for general convex cost functions.
Optimal Control Theory optimizes neural networks, improving robustness and efficiency.
problem Optimizing deep neural networks (DNNs) for better performance and efficiency.
method Integrating Optimal Control Theory with Backpropagation to develop a new optimizer.
result Optimal Control Theoretic Neural Optimizer (OCNOpt) improves upon existing methods in robustness and efficiency.
New algorithm reduces dynamic regret without prior function change knowledge.
problem Non-stationary stochastic optimization with bandit feedback.
method Fixed step sizes combined with multi-scale sampling framework.
result Achieves optimal dynamic regret without prior function change knowledge.
Solves portfolio optimization with costs using numerical methods.
problem Dynamic portfolio optimization with transaction costs and constraints.
method Numerical dynamic programming techniques.
result Problems can now be solved tractably.
Develops RL for dynamic risk assessment in stochastic optimization.
problem Time-consistent risk assessment in stochastic optimization problems.
method Model-free reinforcement learning with dynamic convex risk measures, time-consistent dynamic programming, policy gradient updates, actor-critic neural network optimization.
result Demonstrates optimal policies for statistical arbitrage, financial hedging, and robot control.
DCBO optimizes interventions in evolving causal systems.
problem Optimal interventions in time-varying causal systems.
method Combines sequential decision making, causal inference, and GP emulation.
result DCBO identifies optimal interventions faster than competitors.
New algorithms reduce dynamic regret in non-stationary RL environments.
problem Optimizing policies in environments that change over time.
method POWER and POWER++ algorithms for policy optimization with dynamic regret analysis.
result POWER++ improves dynamic regret by actively adapting to non-stationarity.
New optimization method derived from contact geometry.
problem Optimization problems in machine learning and engineering.
method Contact geometry and dynamical systems.
result Bregman Hamiltonian system can be transformed into separable Hamiltonian.
Optimal reinsurance strategies for multi-line insurance companies.
problem Choosing the best dynamic reinsurance policies for multi-line insurance companies.
method Characterized the optimal survival function as the unique nondecreasing viscosity solution of the HJB equation, solved numerically using the finite difference method.
result Provided proof of convergence of numerical solution to the survival probability function.
GFM models neural network training as a dynamical system to forecast final weights.
problem Computational intensity and inefficiency in training deep neural networks.
method Gradient Flow Matching (GFM) treats training as a dynamical system with learned vector fields.
result GFM achieves forecasting accuracy competitive with Transformer-based models and significantly outperforms classical baselines.
The paper develops methods to estimate optimal treatment sequences under policy constraints.
problem Estimating the best sequence of treatments over multiple stages for individuals.
method Empirical welfare maximization approach, solving treatment assignment sequentially or simultaneously.
result Established convergence rates and upper bounds for estimation methods.
Paper unifies subspace identification and DMD for dynamical systems.
problem Estimating dynamical models from data.
method Unified optimization and regression problems for SID and DMD.
result Proves equivalence of SID and DMD for optimal model construction.
Study dynamic Pareto-optimal allocations in multi-period economies with time-consistent risk measures.
problem Optimal allocation in multi-period pure-exchange economies with stochastic endowments and time-consistent risk measures.
method Introduced dynamic Pareto-optimal allocation processes and derived recursive and comonotone improvement theorems.
result Dynamic Pareto-optimal allocation processes can be constructed recursively and are comonotone.
Paper adds Fisher Information to mean field optimization for faster convergence.
problem Mean field optimization in neural networks training.
method Developed energy-dissipation method and gradient flow on probability space.
result Marginal distributions converge exponentially to minimizer.
This paper presents preliminary work on learning the search heuristic for the optimal motion planning for automated driving in urban traffic. Previous work considered search-based optimal motion planning framework (SBOMP) that utilized numerical or model-based heuristics that did not consider dynamic obstacles. Optimal…
In sequence generation task, many works use policy gradient for model optimization to tackle the intractable backpropagation issue when maximizing the non-differentiable evaluation metrics or fooling the discriminator in adversarial learning. In this paper, we replace policy gradient with proximal policy optimization (…
Study uses SGD to find near-optimal execution cost policies in dynamic markets.
problem Finding optimal execution cost policies in complex markets.
method Stochastic Gradient Descent (SGD) approach to derive near-optimal policies.
result SGD-based policies offer valuable insights and are implementable in volatile markets.
Optimal dynamic fees found for AMMs to deter arbitrageurs and attract noise traders.
problem Optimizing fees in AMMs to balance against arbitrage and noise trading.
method Approximate closed-form solutions to control problem, study of fee structure.
result Two distinct fee regimes identified: high fees to deter arbitrage, low fees to attract noise traders.
Optimizes angular velocity transfers for rigid bodies under deadline constraints.
problem Stochastic guidance of spin states of rigid bodies over a hard deadline.
method Structural analysis of Kantorovich optimal coupling formulation for nonlinear dynamics.
result Derives the ground cost for optimal transport of angular velocity.
KSOS improves kernel learning for dynamical systems via global optimization.
problem Challenges in selecting optimal kernels and tuning parameters in traditional kernel-based methods.
method Global optimization framework with kernel-based surrogate functions.
result KSOS consistently outperforms gradient descent in predicting dynamical systems.
New method optimizes multiple objectives using particle dynamics and gradient flow.
problem Optimizing multiple conflicting objectives in complex scenarios.
method Interacting particle method combining Langevin and birth-death dynamics with a dominance potential.
result Method effectively relocates dominated particles, improving Pareto optimality.
A new model calculates optimal clearing payments in dynamic financial networks.
problem Determining fair clearing payments in networks with potential defaults.
method Extends Eisenberg-Noe model to multiple time periods, solving linear programs for optimal payments.
result Proves the model satisfies the priority of debt claims requirement and finds unique optimal payments.
Optimally explores dynamical systems with varying properties using context inference.
problem Learning dynamics models for systems with varying properties.
method Formulates dynamics models as stochastic processes conditioned on a latent context variable inferred from system transitions. Uses probabilistic formulation to compute optimal action sequences for exploration.
result Demonstrates effectiveness of the method on non-linear toy-problems and reinforcement learning environments.
Study optimal control in unknown nonlinear systems with near-optimal regret bound.
problem Sequential control in unknown, nonlinear dynamical systems.
method LC^3 algorithm, based on information theory.
result Near-optimal O ( T ) O(\sqrt{T}) O ( T ) regret bound for episodic settings. Formulates Markov property for risk-sensitive dynamic optimisation.
problem Risk-sensitive dynamic optimisation problems in discrete time.
method Formulates probabilistic Markov property under dynamic risk framework.
result Property holds for standard risk measures and has multiple equivalent versions.
The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posted a…
New algorithm adapts to unknown demand smoothness for dynamic pricing.
problem Dynamic pricing with unknown Hölder smoothness of demand function.
method Self-similarity condition and adaptive algorithm.
result Adaptive algorithm achieves minimax optimal regret without prior knowledge of smoothness.
Algorithm optimally estimates linear dynamical systems with active input selection.
problem Estimating parameters of linear dynamical systems efficiently.
method Active learning with adaptive input selection.
result Finite time bound and asymptotic optimality proven.
A neural network approach solves dynamic portfolio optimization without dynamic programming.
problem Dynamic portfolio optimization with multiple constraints and high rebalancing frequency.
method Parsimonious neural network without dynamic programming, avoiding high-dimensional expectations.
result Proves convergence to theoretical optimal solution under general conditions.
Method learns optimal treatment sequences from observational data.
problem Optimal dynamic treatment regimes for public policies and medical interventions.
method Doubly robust classification-based approach via backward induction.
result Achieves optimal convergence rate of n^(-1/2) for welfare regret.
Improved algorithm for adaptive dueling bandits with near-optimal regret bound.
problem Non-stationary dueling bandits with unknown number of preference changes.
method Elimination-based rescheduling algorithm for adaptive dynamic regret.
result Near-optimal i l d e O ( S e x t t t C W T ) ilde{O}(\sqrt{S^{ exttt{CW}} T}) i l d e O ( S e x ttt C W T ) dynamic regret bound. Investigates optimal portfolio strategies in markets with latent side information.
problem Investment problem in markets with latent dependence structure and side information.
method Dynamic and constant portfolio strategies, analyzing log-optimal portfolio as benchmark.
result Optimal dynamic strategy growth rate asymptotically converges to constant strategy in stationary markets.
Optimizes dynamic investment portfolios with correlated jumps.
problem Maximizing expected terminal wealth in a multivariate Merton model with dependent jumps.
method Approximating CVaR with comonotonic bounds and maximizing expected terminal wealth.
result Improved optimization of dynamic investment portfolios.
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.
Optimal algorithms for mixable losses in dynamic environments with reduced redundancy.
problem Online optimization of mixable loss functions in a dynamic environment.
method Introduce online mixture schemes with polynomial and logarithmic time complexities.
result Achieves optimal redundancy up to a constant multiplicity gap.
In online learning, the dynamic regret metric chooses the reference (optimal) solution that may change over time, while the typical (static) regret metric assumes the reference solution to be constant over the whole time horizon. The dynamic regret metric is particularly interesting for applications such as online reco…
In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of a bank's work is described in this paper. The problem is then approached using the method of dynamic programming. Dynamic programming m…
Bayesian method estimates dynamics from near-optimal trajectories.
problem Estimating dynamics from near-optimal expert trajectories in reinforcement learning.
method Constraint-based Bayesian approach integrating expert near-optimality.
result Significant improvements in decision-making and transfer success.
This study develops a dynamic inverse optimization framework to recover hidden, time-varying preferences from observed allocation trajectories.
problem The gap between classical optimization theory and real-world practice, especially in the presence of drift and shocks.
method Dynamic inverse optimization framework using a drift-aware estimator grounded in convex analysis and online learning theory.
result Sharp static and dynamic regret bounds for the framework, demonstrating its responsiveness to gradual drift and sudden shocks.
New method learns population dynamics from snapshots using JKO scheme and inverse optimization.
problem Recovering underlying process governing particle evolution from discrete time samples.
method Combines JKO scheme with inverse optimization techniques for end-to-end adversarial training.
result Improved performance over prior JKO-based methods with theoretical guarantees.
The study analyzes momentum-based optimization algorithms from dynamical systems perspective.
problem Understanding convergence rates of momentum-based optimization algorithms.
method Exploits dynamical systems, control theory, and symplectic perspectives to analyze convergence rates.
result Provides closed-form expressions relating algorithm parameters to convergence rates.
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align existing branches of deep learning theory through the lens of dynamical system and …
Study optimal liquidation strategies on Uniswap v2/v3 considering price impact.
problem Optimal liquidation of large positions on Uniswap v2/v3 under transient price impact.
method Dynamic programming and numerical approximation for Uniswap v3, closed-form solutions for v2.
result Obtained optimal strategies for both Uniswap v2 and v3, showing how liquidity profile influences them.