Related papers: A rational logit dynamic for decision-making under…

We study contextual dynamic pricing, where a decision maker posts personalized prices based on observable contexts and receives binary purchase feedback indicating whether the customer's valuation exceeds the price. Each valuation is…

The multi-armed bandit problem is a classical decision-making problem where an agent has to learn an optimal action balancing exploration and exploitation. Properly managing this trade-off requires a correct assessment of uncertainty; in…

Achieving both optimality and safety under unknown system dynamics is a central challenge in real-world deployment of agents. To address this, we introduce a notion of maximum safe dynamics learning, where sufficient exploration is…

Logit dynamics are evolution equations that describe transitions to equilibria of actions among many players. We formulate a pair-wise logit dynamic in a continuous action space with a generalized exponential function, which we call a…

In this paper, we study an ordinary differential equation with a degenerate global attractor at the origin, to which we add a white noise with a small parameter that regulates its intensity. Under general conditions, for any fixed…

Clinical decision requires reasoning in the presence of imperfect data. DTs are a well-known decision support tool, owing to their interpretability, fundamental in safety-critical contexts such as medical diagnosis. However, learning DTs…

In a multi-class classification problem, it is standard to model the output of a neural network as a categorical distribution conditioned on the inputs. The output must therefore be positive and sum to one, which is traditionally enforced…

In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…

Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…

Large annotated datasets inevitably contain noisy labels, which poses a major challenge for training deep neural networks as they easily memorize the labels. Noise-robust loss functions have emerged as a notable strategy to counteract this…

We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use finite temporal logic to express the requirements on the…

Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much…

We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…

This paper surveys some recent developments towards a dynamic quantum logic and outlines its explicite construction -- some analogies and contrasts with other logics of dynamics are indicated. Abstract: The development of ``(static)…

Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations.…

We study stochastic effects on the lagging anchor dynamics, a reinforcement learning algorithm used to learn successful strategies in iterated games, which is known to converge to Nash points in the absence of noise. The dynamics is…

We study the problem of \textit{safe control of linear dynamical systems corrupted with non-stochastic noise}, and provide an algorithm that guarantees (i) zero constraint violation of convex time-varying constraints, and (ii) bounded…

This paper investigates the finite time stabilization problem for a class of nonlinear systems with unknown control directions and unstructured uncertainties. The unstructured uncertainties indicate that not only the parameters but also the…

In this paper, we characterize the noise of stochastic gradients and analyze the noise-induced dynamics during training deep neural networks by gradient-based optimizers. Specifically, we firstly show that the stochastic gradient noise…

This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…