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%matplotlib inline

import matplotlib.pyplot as plt
import seaborn as sns

from IPython.display import Image

Chapter 8 Planning and Learning with Tabular Methods

  • Model-based methods: planning
  • Model-free methods: learning

the heart of both kinds of methods is the computation of value functions.

8.1 Models and Planning

  • a model of the enviroment: anything that an agent can use to predict how the environment will respond to its actions.

    • model can be used to simulate the environemt and produce simulated experience.
  • distribution models: produce a descripiton of all possibilities and their probabilities.

  • sample models: produce just one of the possibilities, sampled according to the probabilities.
\begin{equation*} \text{model} \xrightarrow{\text{planning}} \text{policy} \end{equation*}
  • state-space planning: search through the state space for an optimal policy or an optimal path to a goal.
  • plan-space planning: search through the space of plans. includes: evolutionary methods, partial-order planning.

common structure shared by all state-space planning methods:

\begin{equation*} \text{model} \longrightarrow \text{simulated experience} \xrightarrow{\text{backups}} \text{values} \longrightarrow \text{policy} \end{equation*}

planning uses simulated experience VS learning uses real experience.

8.2 Dyna: Integrating Planning, Acting, and Learning

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Learning and planning are deeply integrated in the sense that they share almost all the same machinery, differing only in the source of their experience.

  • Indirect methods: make fuller use of a limited amount of experiences.
  • Direct methods: much simpler and are not effected by biases in the design of the model.

8.3 When the Model Is Wrong

Models may be incorrect because:

  • Environment is stochastic and only a limited number of samples have been observed;
  • The model was learned using function approximation that has generalized imperfectly;
  • Then environment has changed and its new behavior has not yet been observed:
    • original optimial solution doesn't work any more.
    • better solution exists after environemt changed.

=> conflict between exploration and exploitation => simple heuristics are often effective.

Dyna-Q+ agen: keeps track for each state-action pair. The more time that has elapsed, the greater the chance to be picked next time => special "bonus reward": $r + k \sqrt{\tau}$

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8.4 Prioritized Sweeping

uniform selection is usually not the best; planning can be much more efficient if simulated transitions and updates are focused on particular state-action pairs.

backward focusing of planning computations: work backward from aribitary states that have changed in value. (propagation)

prioritized sweeping: prioritize the updates according to a measure of their urgency, and perform them in order of priority.

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8.5 Expected vs. Sample Updates

Three questions:

  1. Whether the algorithm updates state values $v$, or action values $q$?
  2. Whether the algorithm estimates the value for the optimal policy $\ast$, or for an arbitrary given policy $\pi$?
  3. Whether the updates are expected updates, or sample updates?
    • expected updates: better estimate (uncorrupted by sampling error), but more computation.
    • sample updates: superior on problems with large stochastic branching factors and too many states to be solved exactly.
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8.6 Trajectory Sampling

Two ways of distributing updates:

  • classical approach: sweeps through the entire state space, updating each state once per sweep.
  • sample from the state according to some distribution.
    • trajectory sampling: one simulates explicit individual trajectories and performs updates at the state encountered along the way.

8.7 Real-time Dynamic Programming

8.8 Planning at Decision Time

  • background planning: using simulated experience to gradually improve a policy or value function.
  • decision-time planning: using simulated experience to select an action for the current state. (look much deeper than on-step-ahead and evaluate action choices leading to many different predicted state and reward trajectories).

8.10 Rollout Algorithms

Summary of Part I: Dimensions

three key ideas in common:

  1. seek to estimate value functions;
  2. operate by backing up values along actual or possible state trajectories;
  3. follow the general strategy of generalized policy iteration(GPI).

important dimensions along wich the methods vary:

  • whether they are sample updates or expected updates.
  • the depth of updates (to the degree of boostrapping).
  • on-policy or off-policy.
  • fuction approximation.