Related papers: Optimizing Automatic Differentiation with Deep Rei…

Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…

Computing the Jacobian of the solution of an optimization problem is a central problem in machine learning, with applications in hyperparameter optimization, meta-learning, optimization as a layer, and dataset distillation, to name a few.…

Many optimization problems require balancing multiple conflicting objectives. As gradient descent is limited to single-objective optimization, we introduce its direct generalization: Jacobian descent (JD). This algorithm iteratively updates…

Most nonlinear partial differential equation (PDE) solvers require the Jacobian matrix associated to the differential operator. In PETSc, this is typically achieved by either an analytic derivation or numerical approximation method such as…

In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For iterative algorithms, implicit differentiation alleviates…

This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing…

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL…

Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable,…

We present two improvements to arithmetic in the Jacobian of global function fields based on the approach of Hess. The first reduces the number of expensive reduction steps by optimizing for typical inputs rather than worst-case behavior,…

Deformable continuum robots (DCRs) present unique planning challenges due to nonlinear deformation mechanics and partial state observability, violating the Markov assumptions of conventional reinforcement learning (RL) methods. While…

Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by…

A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters.…

Fractional-order differentiation has many characteristics different from integer-order differentiation. These characteristics can be applied to the optimization algorithms of artificial neural networks to obtain better results. However, due…

Branch-and-bound is a systematic enumerative method for combinatorial optimization, where the performance highly relies on the variable selection strategy. State-of-the-art handcrafted heuristic strategies suffer from relatively slow…

Deep neural networks, particularly in vision tasks, are notably susceptible to adversarial perturbations. To overcome this challenge, developing a robust classifier is crucial. In light of the recent advancements in the robustness of…

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically…

Algorithm unrolling is ubiquitous in machine learning, particularly in hyperparameter optimization and meta-learning, where Jacobians of solution mappings are computed by differentiating through iterative algorithms. Although unrolling is…

Optimal execution is a sequential decision-making problem for cost-saving in algorithmic trading. Studies have found that reinforcement learning (RL) can help decide the order-splitting sizes. However, a problem remains unsolved: how to…

This study proposes a simple procedure to compute Efficient Pseudo Likelihood (EPL) estimator proposed by Dearing and Blevins (2024) for estimating dynamic discrete games, without computing Jacobians of equilibrium constraints. EPL…