Related papers: The Algorithmic Regulator
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…
Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…
Despite their apparent diversity, modern machine learning methods can be reduced to a remarkably simple core principle: learning is achieved by continuously optimizing parameters to minimize or maximize a scalar objective function. This…
The internal model principle states that all robustly regulating controllers must contain a suitably reduplicated internal model of the signal to be regulated. Using frequency domain methods, we show that the number of the copies may be…
We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
We consider a class of optimal control problems on networks that generically permits a reduction to a universal set of reference problems without differential constraints that may be solved analytically. The derivation shows that input…
I discuss several aspects of information theory and its relationship to physics and neuroscience. The unifying thread of this somewhat chaotic essay is the concept of Kolmogorov or algorithmic complexity (Kolmogorov Complexity, for short).…
A principal designs an algorithm that generates a publicly observable prediction of a binary state. She must decide whether to act directly based on the prediction or to delegate the decision to an agent with private information but…
Regulatory networks describe the interactions between molecular or cellular regulators, like transcription factors and genes in gene regulatory networks, kinases and their receptors in signalling networks, or neurons in neural networks. A…
In various contexts in mathematical physics one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…
As AI systems move from generating text to accomplishing goals through sustained interaction, the ability to model environment dynamics becomes a central bottleneck. Agents that manipulate objects, navigate software, coordinate with others,…
We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear…
In Optimal Recovery, the task of learning a function from observational data is tackled deterministically by adopting a worst-case perspective tied to an explicit model assumption made on the functions to be learned. Working in the…
Continuous control and planning remains a major challenge in robotics and machine learning. Neuroscience offers the possibility of learning from animal brains that implement highly successful controllers, but it is unclear how to relate an…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
Reinforcement Learning has emerged as a promising framework for developing adaptive and data-driven strategies, enabling market makers to optimize decision-making policies based on interactions with the limit order book environment. This…
Machine Learning (ML) algorithms shape our lives. Banks use them to determine if we are good borrowers; IT companies delegate them recruitment decisions; police apply ML for crime-prediction, and judges base their verdicts on ML. However,…
In this paper, the classical algebraic regulator problem is studied in a data-driven context. The endosystem is assumed to be an unknown system that is interconnected to a known exosystem that generates disturbances and reference signals.…