S. Rasoul Etesami

Jafar Abbaszadeh Chekan, S. Rasoul Etesami, Cedric Langbort

We consider learning-based control in LQR setting, where the parameters associated with each mode are a priori unknown. The next mode to be activated is revealed online only at the time of switching. The objective is to determine both the switching times and the control gains for each mode such that (1) the norm of the system state remains bounded according to a prescribed criterion, and (2) the accumulated cost is minimized. To formalize the state-norm requirement, we introduce the notion of $(α,β)$-controllability for given parameters $α$ and $β$. We first study the problem in a known model setting and show that, under the switching mechanism described above and under the assumption that each mode is visited infinitely often, the strategy that minimizes the average expected cost consists of applying, in each mode, the feedback gain obtained from the solution of the discrete algebraic Riccati equation, while selecting dwell times that sufficiently satisfy the controllability condition. We refer to this strategy as the benchmark policy. Next, we propose an algorithm for the unknown-model setting that minimizes the regret, defined as the difference between the cumulative cost incurred by the online algorithm and that of the offline benchmark. By accurately estimating dwell-time errors, our method achieves an expected regret of $\mathcal{O}(|\mathcal{M}|^{1/4} n_s^{3/4} + n_m)$, where $n_s$ denotes the number of switches, $|\mathcal{M}|$ is the number of modes, and $n_m$ is the number of malignant switches.

Fatemeh Fardno, S. Rasoul Etesami

The Ethereum blockchain utilizes the EIP-1559 algorithm to manage transaction inclusion and block assembly. However, EIP-1559 and much of the existing literature study this problem from a static perspective, focusing on price evolution without modelling transaction dynamics within the mempool. Motivated by this limitation, we study a dynamic transaction scheduling problem in which transactions with heterogeneous sizes and per-unit values arrive over time and remain in the mempool until scheduled. To capture the stochastic mempool evolution, we formulate the problem as a Markov Decision Process (MDP) whose state represents the mempool configuration and whose actions correspond to block prices. We first provide a primal-dual interpretation of the static EIP-1559 mechanism, showing that block prices arise naturally as dual variables of a social-welfare maximization problem. Building on this perspective, we extend the framework to the dynamic setting and formulate an objective that maximizes long-run discounted reward while incorporating holding costs and overshoot penalties. We then employ a Natural Policy Gradient (NPG) algorithm to compute the optimal policy. Our results show that dynamic pricing stabilizes the mempool while maximizing long-run discounted reward. In particular, as the overshoot penalty increases, the average scheduled transaction volume converges to the target block capacity, and the resulting NPG updates closely resemble the EIP-1559 price update rule. Finally, we study two special cases of the MDP formulation: homogeneous transactions and uniform arrivals. In the homogeneous setting, where the protocol directly controls scheduled volume, we show that the optimal policy has a threshold structure. We then propose a bang-bang pricing mechanism for uniform arrivals and derive a lower bound on the block capacity needed to ensure system stability.