Adversarial Imitation Learning from Incomplete Demonstrations

Imitation learning targets deriving a mapping from states to actions, a.k.a. policy, from expert demonstrations. Existing methods for imitation learning typically require any actions in the demonstrations to be fully available, which is hard to ensure in real applications. Though algorithms for learning with unobservable actions have been proposed, they focus solely on state information and overlook the fact that the action sequence could still be partially available and provide useful information for policy deriving. In this paper, we propose a novel algorithm called Action-Guided Adversarial Imitation Learning (AGAIL) that learns a policy from demonstrations with incomplete action sequences, i.e., incomplete demonstrations. The core idea of AGAIL is to separate demonstrations into state and action trajectories, and train a policy with state trajectories while using actions as auxiliary information to guide the training whenever applicable. Built upon the Generative Adversarial Imitation Learning, AGAIL has three components: a generator, a discriminator, and a guide. The generator learns a policy with rewards provided by the discriminator, which tries to distinguish state distributions between demonstrations and samples generated by the policy. The guide provides additional rewards to the generator when demonstrated actions for specific states are available. We compare AGAIL to other methods on benchmark tasks and show that AGAIL consistently delivers comparable performance to the state-of-the-art methods even when the action sequence in demonstrations is only partially available.Comment: Accepted to International Joint Conference on Artificial Intelligence (IJCAI-19

The largest singletons of set partitions

Recently, Deutsch and Elizalde studied the largest and the smallest fixed points of permutations. Motivated by their work, we consider the analogous problems in set partitions. Let $A_{n,k}$ denote the number of partitions of $\{1,2,\dots, n+1\}$ with the largest singleton $\{k+1\}$ for $0\leq k\leq n$. In this paper, several explicit formulas for $A_{n,k}$, involving a Dobinski-type analog, are obtained by algebraic and combinatorial methods, many combinatorial identities involving $A_{n,k}$ and Bell numbers are presented by operator methods, and congruence properties of $A_{n,k}$ are also investigated. It will been showed that the sequences $(A_{n+k,k})_{n\geq 0}$ and $(A_{n+k,k})_{k\geq 0}$ (mod $p$) are periodic for any prime $p$, and contain a string of $p-1$ consecutive zeroes. Moreover their minimum periods are conjectured to be $N_p=\frac{p^p-1}{p-1}$ for any prime $p$.Comment: 14page

Searches for the Anomalous FCNC Top-Higgs Couplings with Polarized Electron Beam at the LHeC

In this paper, we study the single top and Higgs associated production $\rm e^- p\rightarrow \nu_e \bar{t} \rightarrow \nu_e h \bar{q}(h\rightarrow b\bar{b})$ in the top-Higgs FCNC couplings at the LHeC with the electron beam energy of $E_{e}$ = 60 GeV and $E_{e}$ = 120 GeV, combination of a 7 TeV and 50 TeV proton beam. With the possibility of e-beam polarization ($p_{e}$ = 0, $\pm0.6$), we distinct the Cut-based method and the Multivariate Analysis (MVA) based method, and compare with the current experimental and theoretical limits. It is shown that the branching ratio Br $\rm(t\to uh)$ can be probed to 0.113 (0.093) $\%$, 0.071 (0.057) $\%$, 0.030 (0.022) $\%$ and 0.024 (0.019) $\%$ with the Cut-based (MVA-based) analysis at ($E_{p}$, $E_{e}$) = (7 TeV, 60 GeV), ($E_{p}$, $E_{e}$) = (7 TeV, 120 GeV), ($E_{p}$, $E_{e}$) = (50 TeV, 60 GeV) and ($E_{p}$, $E_{e}$) = (50 TeV, 120 GeV) beam energy and 1$\sigma$ level. With the possibility of e-beam polarization, the expected limits can be probed down to 0.090 (0.073) $\%$, 0.056 (0.045) $\%$, 0.024 (0.018) $\%$ and 0.019 (0.015) $\%$, respectively.Comment: 13pages, 5 figures. Advance in High Energy Physic

CHUNG-YAU INVARIANTS AND RANDOM WALK ON GRAPHS

The Chung-Yau graph invariants were originated from Chung-Yau’s work on discrete Green’s function. They are useful to derive explicit formulas and estimates for hitting times of random walks on discrete graphs. In this thesis, we study properties of Chung-Yau invariants and apply them to study some questions: (1) The relationship of Chung-Yau invariants to classical graph invariants; (2) The change of hitting times under natural graph operations; (3) Properties of graphs with symmetric hitting times; (4) Random walks on weighted graphs with different weight schemes