Structured state-space models (SSMs) have emerged as a powerful architecture in machine learning and control, featuring stacked layers where each consists of a linear time-invariant (LTI) discrete-time system followed by a nonlinearity. While SSMs offer computational efficiency and excel in long-sequence predictions, their widespread adoption in applications like system identification and optimal control is hindered by the challenge of ensuring their stability and robustness properties. We introduce L2RU, a novel parametrization of SSMs that guarantees input-output stability and robustness by enforcing a prescribed L-2 -bound for all parameter values. This design eliminates the need for complex constraints, allowing unconstrained optimization over L2RUs by using standard methods such as gradient descent. Leveraging tools from system theory and convex optimization, we derive a non-conservative parametrization of square discrete-time LTI systems with a specified L-2-bound, forming the foundation of the L2RU architecture. Additionally, we enhance its performance with a bespoke initialization strategy optimized for long input sequences. Through a system identification task, we validate L2RUs superior performance, showcasing its potential in learning and control applications.
In this paper, the reachability analysis for a class of nonlinear systems is addressed by resorting to a data-driven setting. The resulting approach combines into a unique framework linear time-invariant system behavior, data-driven modeling and reinforcement learning algorithms. This allows to determine inner and outer approximations of the exact predecessor and successor sets, whose accuracy is evaluated by means of statistical tests. Finally, the proposed approach is assessed by resorting to a benchmark example and providing numerical comparisons with a model-based competitor.
In this paper, we show how a separable structure between decision and uncertain variables in the constraints of non-convex robust scenario optimization problems can be exploited to bound the complexity associated with the solution. The resulting bounds are easily computable, and can be solved prior to determining the solution to the non-convex scenario program. Leveraging the scenario approach theory, these bounds can be used to find suitable certifications of the risk (a posteriori, once the scenarios are collected). Furthermore, this result can be exploited to determine the size of the scenario sample necessary to provide a user-chosen reliability level of the solution, for which we discuss both a one-shot and an iterative resolution approach.
The causal conditional (CC) directed information (DI) can test the Granger causality for stochastic processes. However, for point process networks, the CCDI has only been developed for a trivariate network. In this work, we develop the general multivariate CCDI under Kramer’s framework by developing the CC likelihood, which is characterized by marginal intensity functions. We establish several Granger causality equivalences, unifying and generalizing existing results. Further, for Hawkes networks, we develop an estimation method of CCDI requiring only one point process trajectory, by developing an analytical formula for the marginal intensity functions, and an ergodic theorem for the CCDI.
Recently, there has been a surge of interest in decentralized learning approaches to tackle complex collaborative tasks in multi-agent systems. One of the most promising approaches is multi-agent reinforcement learning (MARL). Yet, as the number of agents becomes larger, the sample complexity in MARL increases exponentially, making scalability a fundamental issue. Networked MARL algorithms can address this issue by leveraging a communication network for information exchange between the agents. For homogeneous network MARL, previous research established a regret upper-bound root MH(4)SAT. Recent approaches rely on global knowledge about the structure of the communication network, which poses a serious limitation when it is not known or changes depending on the task. In this paper, we overcome this limitation by proposing a novel networked MARL algorithm with an upper-confidence bound (UCB) exploration strategy, called provably efficient local-information networked (PrELIN) MARL, that does not require any global information but only relies on the local interactions between the agents. Furthermore, we derive the regret and sample complexity for our algorithm and show that the regret bound may still remain sublinear.
