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Title: Surprising Negative Results for Generative  Adversarial Tree Search 

Paper content:
While many recent advances in deep reinforcement learning rely on model-free methods, model-based approaches remain an alluring prospect for their potential to exploit unsupervised data to learn environment dynamics.
One prospect is to pursue hybrid approaches, as in AlphaGo, which combines Monte-Carlo Tree Search (MCTS)—a model-based method—with deep-Q networks (DQNs)—a model-free method.
MCTS requires generating rollouts, which is computationally expensive.
In this paper, we propose to simulate roll-outs, exploiting the latest breakthroughs in image-to-image transduction, namely Pix2Pix GANs, to predict the dynamics of the environment.
Our proposed algorithm, generative adversarial tree search (GATS), simulates rollouts up to a specified depth using both a GAN- based dynamics model and a reward predictor.
GATS employs MCTS for planning over the simulated samples and uses DQN to estimate the Q-function at the leaf states.
Our theoretical analysis establishes some favorable properties of GATS vis-a-vis the bias-variance trade-off and empirical results show that on 5 popular Atari games, the dynamics and reward predictors converge quickly to accurate solutions.
However, GATS fails to outperform DQNs in 4 out of 5 games.
Notably, in these experiments, MCTS has only short rollouts (up to tree depth 4), while previous successes of MCTS have involved tree depth in the hundreds.
We present a hypothesis for why tree search with short rollouts can fail even given perfect modeling.
The earliest and best-publicized applications of deep reinforcement learning (DRL) involve Atari games (Mnih et al., 2015) and the board game of Go (Silver et al., 2016) , where experience is inexpensive because the environments are simulated.
In such scenarios, DRL can be combined with Monte-Carlo tree search (MCTS) methods (Kearns et al., 2002; Kocsis & Szepesvári, 2006) for planning, where the agent executes roll-outs on the simulated environment (as far as computationally feasible) to finds suitable policies.
However, for RL problems with long episodes, e.g. Go, MCTS can be very computationally expensive.
In order to speed up MCTS for Go and learn an effective policy, Alpha Go (Silver et al., 2016 ) employs a depth-limited MCTS with the depth in the hundreds on their Go emulator and use an estimated Q-function to query the value of leaf nodes.
However, in real-world applications, such as robotics (Levine et al., 2016) and dialogue systems (Lipton et al., 2016) , collecting samples often takes considerable time and effort.
In such scenarios, the agent typically cannot access either the environment model or a corresponding simulator.Recently, generative adversarial networks (GANs) BID15 have emerged as a popular tool for synthesizing realistic-seeming data, especially for high-dimensional domains, including images and audio.
Unlike previous approaches to image generation, which typically produced blurry images due to optimizing an L1 or L2 objective, GANs produces crisp images.
Since theire original conception as an unsupervised method, GANs have been extended for conditional generation, e.g., generating an image conditioned on a label (Mirza & Osindero, 2014; Odena et al., 2016) or the next frame in a video given a context window (Mathieu et al., 2015) .
Recently, the PIX2PIX approach has demonstrated impressive results on a range of image-to-image transduction tasks (Isola et al., 2017) .In
this work, we propose and analyze generative adversarial tree search (GATS), a new DRL algorithm that utilizes samples from the environment to learn both a Q-function approximator, a near-term reward predictor, and a GAN-based model of the environment's dynamics (state transitions). Together
, the dynamics model and reward predictor constitute a learned simulator on which MCTS can be performed. GATS leverages
PIX2PIX GANs to learn a generative dynamics model (GDM) that efficiently learns the dynamics of the environment, producing images that agree closely with the actual observed transactions and are also visually crisp. We thoroughly
study various image transduction models, arriving ultimately at a GDM that converges quickly (compared to the DQN), and appears from our evaluation to be reasonably robust to subtle distribution shifts, including some that destroy a DQN policy. We also train
a reward predictor that converges quickly, achieving negligible error (over 99% accuracy). GATS bridges
model-based and model-free reinforcement learning, using the learned dynamics and reward predictors to simulate roll-outs in combination with a DQN. Specifically
, GATS deploys the MCTS method for planning over a bounded tree depth and uses the DQN algorithm to estimate the Q-function as a value for the leaf states (Mnih et al., 2015; Van Hasselt et al., 2016) .One notable
aspect of the GATS algorithm is its flexibility, owing to consisting of a few modular building blocks: (i) value learning
: we deployed DQN and DDQN (ii) planning: we
use pure Monte Carlo sampling; (iii) a reward predictor
: we used a simple 3-class classifier; (iv) dynamics model: we
propose the GDM architecture. Practically, one can swap
in other methods for any among these blocks and we highlight some alternatives in the related work. Thus, GATS constitutes a
general framework for studying the trade-offs between model-based and model-free reinforcement learning.
Discussion of negative results In this section, we enumerate several hypotheses for why GATS under-performs DQN despite near-perfect modeling, and discuss several attempts to improve GATS based on these hypotheses.
The following are shown in TAB1 .
DISPLAYFORM0 Replay Buffer: The agent's decision under GATS sometimes differs from that of the learned Q model.
Therefore, it is important that we allow the Q-learner to observe the outcome of important outcomes in the generated MCTS states.
To address this problem, we tried storing the samples generated in tree search and use them to further train the Q-model.
We studied two scenarios:
(i) using plain DQN with no generated samples and
(ii) using Dyna-Q to train the Q function on the generated samples in MCTS.
However, these techniques did not improve the performance of GATS.Optimizer: Since the problem is slightly different from DQN, especially in the Dyna-Q setting with generated frames, we tried a variety of different learning rates and minibatch sizes to tune the Q-learner.

assistant: text: Surprising negative results on Model Based + Model deep RL