Seungjoon Lee

Nicholas Karris, Evangelos A. Nikitopoulos, Ioannis G. Kevrekidis et al.

We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued analog of Euler's method is first-order accurate when the measure evolves ``smoothly.'' In applications of interest, however, the measure is an empirical distribution of a system of stochastic particles whose behavior is only accessible through an agent-based micro-scale simulation. In such cases, this empirical measure does not evolve smoothly because the individual particles move chaotically on short time scales. However, we can still perform our Euler-type method, and when the particles' collective distribution approximates a measure that \emph{does} evolve smoothly, we observe that the algorithm still accurately predicts this collective behavior over relatively large Euler steps, thus reducing the number of micro-scale steps required to step forward in time. In this way, our algorithm provides a ``macro-scale timestepper'' that requires less micro-scale data to still maintain accuracy, which we demonstrate with three illustrative examples: a biological agent-based model, a model of a PDE, and a model of Langevin dynamics.

Suho Shin, Seungjoon Lee, Jungseul Ok

We consider a multi-armed bandit problem in which a set of arms is registered by each agent, and the agent receives reward when its arm is selected. An agent might strategically submit more arms with replications, which can bring more reward by abusing the bandit algorithm's exploration-exploitation balance. Our analysis reveals that a standard algorithm indeed fails at preventing replication and suffers from linear regret in time $T$. We aim to design a bandit algorithm which demotivates replications and also achieves a small cumulative regret. We devise Hierarchical UCB (H-UCB) of replication-proof, which has $O(\ln T)$-regret under any equilibrium. We further propose Robust Hierarchical UCB (RH-UCB) which has a sublinear regret even in a realistic scenario with irrational agents replicating careless. We verify our theoretical findings through numerical experiments.

Seungjoon Lee, Hyungbo Shim

Economic dispatch problem for a networked power system has been considered. The objective is to minimize the total generation cost while meeting the overall supply-demand balance and generation capacity. In particular, a more practical scenario has been studied by considering the power losses. A non-convex optimization problem has been formulated where the non-convexity comes from the nonlinear equality constraint representing the supply-demand balance with the power losses. It is shown that the optimization problem can be solved using convex relaxation and dual decomposition. A simple distributed algorithm is proposed to solve the optimization problem. Specifically, the proposed algorithm does not require any initialization process and hence robust to various changes in operating condition. In addition, the behavior of the proposed algorithm is analyzed when the problem is infeasible.