Related papers: General non-linear Bellman equations

This paper provides a nonparametric analysis for several classes of models, with cases such as classical measurement error, regression with errors in variables, factor models and other models that may be represented in a form involving…

Successor-style representations have many advantages for reinforcement learning: for example, they can help an agent generalize from past experience to new goals, and they have been proposed as explanations of behavioral and neural data…

This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…

This paper proposes a data-driven systematic, consistent and non-exhaustive approach to Model Selection, that is an extension of the classical agnostic PAC learning model. In this approach, learning problems are modeled not only by a…

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that…

Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…

Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…

We introduce a new algorithm for multi-objective reinforcement learning (MORL) with linear preferences, with the goal of enabling few-shot adaptation to new tasks. In MORL, the aim is to learn policies over multiple competing objectives…

Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the…

Most systems and learning algorithms optimize average performance or average loss -- one reason being computational complexity. However, many objectives of practical interest are more complex than simply average loss. This arises, for…

Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature…

A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization…

Machine Learning is a powerful tool to reveal and exploit correlations in a multi-dimensional parameter space. Making predictions from such correlations is a highly non-trivial task, in particular when the details of the underlying dynamics…

A burgeoning paradigm in algorithm design is the field of algorithms with predictions, in which algorithms can take advantage of a possibly-imperfect prediction of some aspect of the problem. While much work has focused on using predictions…

We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…

When machine-learning algorithms are used in high-stakes decisions, we want to ensure that their deployment leads to fair and equitable outcomes. This concern has motivated a fast-growing literature that focuses on diagnosing and addressing…

In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental…

Designing bounded-memory algorithms is becoming increasingly important nowadays. Previous works studying bounded-memory algorithms focused on proving impossibility results, while the design of bounded-memory algorithms was left relatively…

It is introduced an open class of linear operators on Banach and Hilbert spaces such that their non-wandering set is an infinite dimensional topologically mixing subspace. In certain cases, the non-wandering set coincides with the whole…