README.md

---
tags:
- Pixelcopter-PLE-v0
- reinforce
- reinforcement-learning
- custom-implementation
- deep-rl-class
model-index:
- name: policy_grad_2-Pixelcopter-PLE-v0
  results:
  - task:
      type: reinforcement-learning
      name: reinforcement-learning
    dataset:
      name: Pixelcopter-PLE-v0
      type: Pixelcopter-PLE-v0
    metrics:
    - type: mean_reward
      value: 70.30 +/- 33.94
      name: mean_reward
      verified: false
---

  # **Reinforce** Agent playing **Pixelcopter-PLE-v0**
  This is a trained model of a **Reinforce** agent playing **Pixelcopter-PLE-v0** .
  To learn to use this model and train yours check Unit 4 of the Deep Reinforcement Learning Course: https://huggingface.co/deep-rl-course/unit4/introduction


  # Some math about 'Pixelcopter' training.
The game is to fly in a passage and avoid blocks. Let we have trained our agent so that the probability to crash at block is _p_ (low enogh, I hope).
The probability that the copter crashes exactly at _n_-th block is product of probabilities it doesn't crash at previous _(n-1)_ blocks and probability it crashes at current block:
$$P = {p \cdot (1-p)^{n-1}}$$
The mathematical expectation of number of  the block it crashes at is:
$$<n> = \sum_{n=1}^\infty{n \cdot p \cdot (1-p)^{n-1}} = \frac{1}{p}$$
The std is:
$$std(n) = \sqrt{<n^2>-<n>^2}$$
$$<n^2> = \sum_{n=1}^\infty{n^2 \cdot p \cdot (1-p)^{n-1}} = \frac{2-p}{p^2}$$
$$std(n) = \sqrt{\frac{2-p}{p^2}-\left( \frac{1}{p} \right) ^2} = \frac{\sqrt{1-p}}{p}$$
So difference is:
$$<n> - std(n) = \frac{1 - \sqrt{1-p}}{p}$$
As long as
$$ 0 \le p \le 1 $$
the following is true:
$$\sqrt{1-p} \ge 1-p$$
$$<n> - std(n) = \frac{1 - \sqrt{1-p}}{p} \le \frac{1 - (1-p)}{p} = 1$$
The scores _s_ in 'Pixelcopter' are the number of blocks passed decreased by 5 (for crash). So the average is lower by 5 and the std is the same. No matter how small _p_ is, our 'least score' is:
$$ (<n> - 5) - std(n) = <n> - std(n) - 5 \le - 4$$
But as we use only 10 episodes to calculate statistics and episode duration is limited, we can still achieve the goal, better agent, more chances. But understanding this is disappointing