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As shown in the main text, under the assumption that the influence network is unbiased, our factor baselines are indeed valid control variates. We prove this result below, repeating the statement itself for posterity and providing a supplementary lemma on control variates as a restatement of known results. Let X, Y and Zbe random variables where the law of Xconditional on Z is denoted Pθ(X|Z), and Y is independent of X conditioned on Z; i.e. Then, we have that E[Y θln Pθ(X)] = 0. Proof. Factor baselines are valid control variates if GΣ is true to the MDP (i.e.

A.1 Proof of Theorem 1 To prove Theorem 1, we need the help of the following Lemma See Proposition 7.1 in [3]. Now we can prove our Theorem 1. Proof. For games with only one step (normal-form games, functional-form games), there is only one fixed state. Therefore, the distribution of state-action is equivalent to the distribution of the action. A.2 Proof of Theorem 2 Let us restate our Theorem 2 Theorem 2. For a given empirical payoff matrix A RM N and the reward vector aM+1 for policy M + ||(I A>(A>))aM+1||2, (18) where (A>) is the Moore-Penrose pseudoinverse of A>, and σmin(A) is the minimum singular value of A. Proof. The last equation comes from the analytic calculation of min1>β=1 ||β (A>) aM+1||2 using Lagrangian.

DNN pruning is an approach for deep model compression, which aimsateliminating someparameters withtolerable performance degradation.

Here, we show how to benefit from the flexibility of RNNs while representing individual differences inalow-dimensional andinterpretable space. Toachievethis, wepropose anovelend-to-end learning frameworkinwhich an encoder istrained to map the behavior of subjects into alow-dimensional latent space.

To achieve both efficient and high-quality synthesis, various distillation-based accelerated sampling methods have been developed recently.