Related papers: On the relation between dynamic regret and closed-…
An example of a time-invariant time-delay system that is uniformly globally attractive and exponentially stable, hence forward complete, but whose reachability sets from bounded initial conditions are not bounded over compact time intervals…
We study the problem of online learning and online regret minimization when samples are drawn from a general unknown non-stationary process. We introduce the concept of a dynamic changing process with cost $K$, where the conditional…
We prove non-asymptotic lower bounds on the expectation of the maximum of $d$ independent Gaussian variables and the expectation of the maximum of $d$ independent symmetric random walks. Both lower bounds recover the optimal leading…
Given data generated by an observable stochastic process, we study how to construct statistically optimal decisions for general stochastic optimization problems. Our setting encompasses non-standard data structures, including data…
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which…
Standard problem of one-degree-of-freedom mechanical systems with Coulomb friction is revised for a relay-based feedback stabilization. It is recalled that such a system with Coulomb friction is asymptotically stabilizable via a relay-based…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
Classical stability theory for stochastic programming relies on the Wasserstein-Fortet-Mourier duality, which requires the ground cost to be a distance. When using problem-dependent costs instead of metrics, this duality no longer yields…
In this study, I investigate the dynamic decision problem with a finite parameter space when the functional form of conditional expected rewards is misspecified. Traditional algorithms, such as Thompson Sampling, guarantee neither an…
How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a…
We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
We study the dynamic regret of multi-armed bandit and experts problem in non-stationary stochastic environments. We introduce a new parameter $\Lambda$, which measures the total statistical variance of the loss distributions over $T$ rounds…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
We study dynamic regret minimization in non-stationary online learning, with a primary focus on follow-the-regularized-leader (FTRL) methods. FTRL is important for curved losses and for understanding adaptive optimizers such as Adam, yet…
We study episodic linear mixture MDPs with the unknown transition and adversarial rewards under full-information feedback, employing dynamic regret as the performance measure. We start with in-depth analyses of the strengths and limitations…
Non-stationary multi-armed bandits enable agents to adapt to changing environments by incorporating mechanisms to detect and respond to shifts in reward distributions, making them well-suited for dynamic settings. However, existing…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Linear dynamical systems that obey stochastic differential equations are canonical models. While optimal control of known systems has a rich literature, the problem is technically hard under model uncertainty and there are hardly any…
We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed even if the linearization at the desired set point fails to be stabilizable. Therefore, we…