A Regularized Opponent Model with Maximum Entropy Objective

In a single-agent setting, reinforcement learning (RL) tasks can be cast into an inference problem by introducing a binary random variable o, which stands for the "optimality". In this paper, we redefine the binary random variable o in multi-agent setting and formalize multi-agent reinforcement learning (MARL) as probabilistic inference. We derive a variational lower bound of the likelihood of achieving the optimality and name it as Regularized Opponent Model with Maximum Entropy Objective (ROMMEO). From ROMMEO, we present a novel perspective on opponent modeling and show how it can improve the performance of training agents theoretically and empirically in cooperative games. To optimize ROMMEO, we first introduce a tabular Q-iteration method ROMMEO-Q with proof of convergence. We extend the exact algorithm to complex environments by proposing an approximate version, ROMMEO-AC. We evaluate these two algorithms on the challenging iterated matrix game and differential game respectively and show that they can outperform strong MARL baselines.Comment: Accepted to International Joint Conference on Artificial Intelligence (IJCA2019

B\to X_s\gamma, X_s l^+ l^- decays and constraints on the mass insertion parameters in the MSSM

In this paper, we study the upper bounds on the mass insertion parameters $(\delta^{q}_{AB})_{ij}$ in the minimal supersymmetric standard model (MSSM). We found that the information from the measured branching ratio of $B \to X_s l^+ l^-$ decay can help us to improve the upper bounds on the mass insertions parameters \left (\delta^{u,d}_{AB})_{3j,i3}. Some regions allowed by the data of $Br(B \to X_s \gamma)$ are excluded by the requirement of a SM-like $C_{7\gamma}(m_b)$ imposed by the data of $Br(B \to X_s l^+ l^-)$.Comment: 16 pages, 5 eps figure files, typos remove

5-Fluoro-1H-indole-3-carb­oxy­lic acid

In the title compound, C9H6FNO2, the carboxyl group is twisted slightly away from the indole-ring plane [dihedral angle = 7.39 (10)°]. In the crystal, carboxyl inversion dimers linked by pairs of O—H⋯O hydrogen bonds generate R 2 2(8) loops and N—H⋯O hydrogen bonds connect the dimers into (10) sheets