Restricted modules and associated vertex algebras of extended Heisenberg-Virasoro algebra

In this paper, a family of infinite dimensional Lie algebras $\tilde{\mathcal{L}}$ is introduced and investigated, called the extended Heisenberg-Virasoro algebra,denoted by $\tilde{\mathcal{L}}$. These Lie algebras are related to the $N=2$ superconformal algebra and the Bershadsky-Polyakov algebra. We study restricted modules and associated vertex algebras of the Lie algebra $\tilde{\mathcal{L}}$. More precisely, we construct its associated vertex (operator) algebras $V_{\tilde{\mathcal{L}}}(\ell_{123},0)$, and show that the category of vertex algebra $V_{\tilde{\mathcal{L}}}(\ell_{123},0)$-modules is equivalent to the category of restricted $\tilde{\mathcal{L}}$-modules of level $\ell_{123}$.Then we give uniform constructions of simple restricted $\tilde{\mathcal{L}}$-modules. Also, we present several equivalent characterizations of simple restricted modules over $\tilde{\mathcal{L}}$.Comment: 22 page

Study of photon detection efficiency and position resolution of BESIII electromagnetic calorimeter

We study the photon detection efficiency and position resolution of the electromagnetic calorimeter (EMC) of the BESIII experiment. The control sample of the initial-state-radiation (ISR) process of $e^+e^-\rightarrow \gamma \mu^+\mu^-$ is used at $J/\psi$ and $\psi(3770)$ resonances for the EMC calibration and photon detection efficiency study. Photon detection efficiency is defined as the predicted photon, obtained by performing a kinematic fit with two muon tracks, matched with real photons in the EMC. The spatial resolution of the EMC is defined as the separation in polar ($\theta$) and azimuthal ($\phi$) angles between charged track and associated cluster centroid on the front face of the EMC crystals.Comment: 5 page

Online Meta-Critic Learning for Off-Policy Actor-Critic Methods

Off-Policy Actor-Critic (Off-PAC) methods have proven successful in a variety of continuous control tasks. Normally, the critic's action-value function is updated using temporal-difference, and the critic in turn provides a loss for the actor that trains it to take actions with higher expected return. In this paper, we introduce a novel and flexible meta-critic that observes the learning process and meta-learns an additional loss for the actor that accelerates and improves actor-critic learning. Compared to the vanilla critic, the meta-critic network is explicitly trained to accelerate the learning process; and compared to existing meta-learning algorithms, meta-critic is rapidly learned online for a single task, rather than slowly over a family of tasks. Crucially, our meta-critic framework is designed for off-policy based learners, which currently provide state-of-the-art reinforcement learning sample efficiency. We demonstrate that online meta-critic learning leads to improvements in avariety of continuous control environments when combined with contemporary Off-PAC methods DDPG, TD3 and the state-of-the-art SAC.Comment: NeurIPS 202

Dynamic Memory-based Curiosity: A Bootstrap Approach for Exploration

The sparsity of extrinsic rewards poses a serious challenge for reinforcement learning (RL). Currently, many efforts have been made on curiosity which can provide a representative intrinsic reward for effective exploration. However, the challenge is still far from being solved. In this paper, we present a novel curiosity for RL, named DyMeCu, which stands for Dynamic Memory-based Curiosity. Inspired by human curiosity and information theory, DyMeCu consists of a dynamic memory and dual online learners. The curiosity arouses if memorized information can not deal with the current state, and the information gap between dual learners can be formulated as the intrinsic reward for agents, and then such state information can be consolidated into the dynamic memory. Compared with previous curiosity methods, DyMeCu can better mimic human curiosity with dynamic memory, and the memory module can be dynamically grown based on a bootstrap paradigm with dual learners. On multiple benchmarks including DeepMind Control Suite and Atari Suite, large-scale empirical experiments are conducted and the results demonstrate that DyMeCu outperforms competitive curiosity-based methods with or without extrinsic rewards. We will release the code to enhance reproducibility