Experiment 5 · breakout · fresh

YOUR TASK: write, from scratch, the weights of a policy network that plays this game as well as possible. There is no training: no data, no loss, no gradients, no fine-tuning; you choose every number yourself. You have no tools: no code execution, no calculator, nothing to run. This is a single response and you will get no feedback. First describe your design briefly (the strategy, and what the hidden units compute), then write the edits block.

THE GAME: Breakout from MinAtar (Young & Tian 2019), on a 10 x 10 grid. The player moves a one-cell paddle along the bottom row and must bounce a ball to break 3 rows of bricks near the top. Each brick broken gives +1; when all bricks are cleared, 3 new rows appear. The ball moves only diagonally; when it hits the paddle it is sent up to the left or to the right depending on the side of the paddle it hits; it is reflected by walls and bricks. The episode ends when the ball reaches the bottom row without being caught.
Actions: left and right move the paddle; up, down and fire do nothing (they act as no-op).

The game's exact implementation (the MinAtar package, version 1.0.15, file minatar/environments/breakout.py) follows. The environment wrapper calls act(a) with a = 0..5 meaning 'n' (no-op), 'l', 'u', 'r', 'd', 'f' (this file's action_map), and with probability 0.1 it repeats the previous action instead of the new one (sticky actions). The observation the network gets is built from this file's state() as described under THE INPUT.

```python
################################################################################################################
# Authors:                                                                                                     #
# Kenny Young (kjyoung@ualberta.ca)                                                                            #
# Tian Tian (ttian@ualberta.ca)                                                                                #
################################################################################################################
import numpy as np


#####################################################################################################################
# Env
#
# The player controls a paddle on the bottom of the screen and must bounce a ball tobreak 3 rows of bricks along the
# top of the screen. A reward of +1 is given for each brick broken by the ball.  When all bricks are cleared another 3
# rows are added. The ball travels only along diagonals, when it hits the paddle it is bounced either to the left or
# right depending on the side of the paddle hit, when it hits a wall or brick it is reflected. Termination occurs when
# the ball hits the bottom of the screen. The balls direction is indicated by a trail channel.
#
#####################################################################################################################
class Env:
    def __init__(self, ramping=None):
        self.channels ={
            'paddle':0,
            'ball':1,
            'trail':2,
            'brick':3,
        }
        self.action_map = ['n','l','u','r','d','f']
        self.random = np.random.RandomState()
        self.reset()

    # Update environment according to agent action
    def act(self, a):
        r = 0
        if(self.terminal):
            return r, self.terminal

        a = self.action_map[a]

        # Resolve player action
        if(a=='l'):
            self.pos = max(0, self.pos-1)
        elif(a=='r'):
            self.pos = min(9,self.pos+1)

        # Update ball position
        self.last_x = self.ball_x
        self.last_y = self.ball_y
        if(self.ball_dir == 0):
            new_x = self.ball_x-1
            new_y = self.ball_y-1
        elif(self.ball_dir == 1):
            new_x = self.ball_x+1
            new_y = self.ball_y-1
        elif(self.ball_dir == 2):
            new_x = self.ball_x+1
            new_y = self.ball_y+1
        elif(self.ball_dir == 3):
            new_x = self.ball_x-1
            new_y = self.ball_y+1

        strike_toggle = False
        if(new_x<0 or new_x>9):
            if(new_x<0):
                new_x = 0
            if(new_x>9):
                new_x=9
            self.ball_dir=[1,0,3,2][self.ball_dir]
        if(new_y<0):
            new_y = 0
            self.ball_dir=[3,2,1,0][self.ball_dir]
        elif(self.brick_map[new_y,new_x]==1):
            strike_toggle = True
            if(not self.strike):
                r+=1
                self.strike = True
                self.brick_map[new_y,new_x]=0
                new_y = self.last_y
                self.ball_dir=[3,2,1,0][self.ball_dir]
        elif(new_y == 9):
            if(np.count_nonzero(self.brick_map)==0):
                self.brick_map[1:4,:] = 1
            if(self.ball_x == self.pos):
                self.ball_dir=[3,2,1,0][self.ball_dir]
                new_y = self.last_y
            elif(new_x == self.pos):
                self.ball_dir=[2,3,0,1][self.ball_dir]
                new_y = self.last_y
            else:
                self.terminal = True

        if(not strike_toggle):
            self.strike = False

        self.ball_x = new_x
        self.ball_y = new_y
        return r, self.terminal

    # Query the current level of the difficulty ramp, difficulty does not ramp in this game, so return None
    def difficulty_ramp(self):
        return None

    # Process the game-state into the 10x10xn state provided to the agent and return
    def state(self):
        state = np.zeros((10,10,len(self.channels)),dtype=bool)
        state[self.ball_y,self.ball_x,self.channels['ball']] = 1
        state[9,self.pos, self.channels['paddle']] = 1
        state[self.last_y,self.last_x,self.channels['trail']] = 1
        state[:,:,self.channels['brick']] = self.brick_map
        return state

    # Reset to start state for new episode
    def reset(self):
        self.ball_y = 3
        ball_start = self.random.randint(2)
        self.ball_x, self.ball_dir = [(0,2),(9,3)][ball_start]
        self.pos = 4
        self.brick_map = np.zeros((10,10))
        self.brick_map[1:4,:] = 1
        self.strike = False
        self.last_x = self.ball_x
        self.last_y = self.ball_y
        self.terminal = False

    # Dimensionality of the game-state (10x10xn)
    def state_shape(self):
        return [10,10,len(self.channels)]

    # Subset of actions that actually have a unique impact in this environment
    def minimal_action_set(self):
        minimal_actions = ['n','l','r']
        return [self.action_map.index(x) for x in minimal_actions]

```

THE INPUT (600 numbers, each 0 or 1): the 10 x 10 grid (rows 0 top to 9 bottom, columns 0 left to 9 right) with 6 channels. Input number i = (row * 10 + column) * 6 + channel; for example input 0 is (row 0, column 0, channel 0), input 6 is (row 0, column 1, channel 0) and input 599 is (row 9, column 9, channel 5). In this game:
  channel 0 (player): the paddle
  channel 1 (danger): always empty in this game
  channel 2 (reward): the bricks
  channel 3 (projectile): the ball
  channel 4 (trail): the ball's previous cell (it shows which way the ball moves)
  channel 5 (gauge): always empty in this game
THE OUTPUT (6 numbers, logits) for the actions 0 no-op, 1 left, 2 up, 3 right, 4 down, 5 fire; the action is sampled from the softmax of the logits. With probability 0.1 the game repeats the previous action instead (sticky actions).
How the 6 channels are built from the game's own channels (state() in the source): channel 0 (player) <- paddle; channel 1 (danger) <- nothing; channel 2 (reward) <- brick; channel 3 (projectile) <- ball; channel 4 (trail) <- trail; channel 5 (gauge) <- nothing. A cell is 1 in a channel if any of its source channels is 1.

THE NETWORK (the same architecture as the reinforcement-learning networks it will be compared with): a multilayer perceptron with 600 inputs, two hidden layers of 32 units with tanh activations, and 6 outputs; 20,486 parameters:
  h1 = tanh(x @ W1 + b1)          W1: 600 x 32, b1: 32
  h2 = tanh(h1 @ W2 + b2)         W2: 32 x 32,  b2: 32
  logits = h2 @ W3 + b3           W3: 32 x 6,  b3: 6
Row i of W1 holds the weights from input i to the 32 first-layer units; column j of a weight matrix belongs to unit j of the next layer. EVERY WEIGHT STARTS AT 0; you set the weights you need.

HOW YOUR NETWORK IS SCORED: its mean score per episode over 1,000 episodes, each action sampled from the softmax of the logits (with the sticky actions above); an episode also stops after 10,000 steps. It is compared with networks of the same architecture trained by reinforcement learning on this game.

HOW TO WRITE THE WEIGHTS (numbers only; nothing is run). Write a code block whose opening line is three backticks followed by the word edits, one statement per line ('#' starts a comment; a long list may continue over the next lines). Tensors: W1, b1, W2, b2, W3, b3.

```edits
W1[12, 0] = 2.5                     # one entry: row 12, column 0
W1[0:6, 3] = [1, 0, -1, 0, 2, 0]    # explicit values along a range (as many values as entries)
b1[0:4] = -1                        # fill a range (a:b is half-open; ':' alone = the whole axis)
W1[3:600:60, 0] = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1]   # column 0 of channel 3, rows 0..9 of the grid -> unit 0
W2[0:2, 0:3] = [[1, -1, 0.5], [0, 2, 0]]   # a 2-D list for a 2-D block (here 2 x 3)
W3[:, 2] *= 2                       # scale (also += and -=)
```
Ranges: a:b is half-open, a:b:s takes every s-th index. Input index i = (row * 10 + column) * 6 + channel. Useful strided ranges: all 10 cells of column c in channel ch are rows c*6+ch : 600 : 60 of W1; all 10 cells of row r in channel ch are rows r*60+ch : r*60+60 : 6.
Statements apply in order; a later statement overwrites an earlier one. Only the LAST edits block of your reply is read; a statement that cannot be read is skipped (the others still apply). Values: plain decimal numbers (|v| <= 1e6).

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**Designing a hand-tuned policy**
**Designing trajectory inference**
**Estimating reflected landing**

**Analyzing paddle targeting**
**Refining bounce detection**
**Designing vertical bounce logic**

**Deriving reflected target formula**
**Deriving right-move thresholds**

**Deriving safe paddle bounds**
**Deriving threshold comparisons**

**Allocating movement thresholds**
**Tuning movement policy**
**Augmenting near-bounce priority**

**Refining paddle positioning**
**Selecting directional center**
**Validating directional center**

**Choosing row 3 centers**
**Choosing safe-set policy**
**Refining bounce-direction policy**

**Choosing safe alternate cells**
**Adding safe catch swaps**
**Classifying safe catch moves**

**Defining step thresholds**
**Designing movement logits**

**Tuning paddle response thresholds**
**Tuning bounce-state inference**
**Writing W1 row weights**

**Writing thresholded gating updates**
**Preparing first-layer weights**

**Grouping weights by symmetry**
**Grouping W1 by symmetry**

**Preparing W1 weight assignments**
**Mapping control units**

**Centering paddle for landing**
**Adjusting paddle center target**

**Setting paddles 7,2**
**Maintaining paddles 7,2**

**Exploring ball trajectories**
**Refining intercept prediction**

**Analyzing paddle reversals**
**Tuning paddle steering**

**Refining wall-collision handling**
**Refining wall-edge steering**

**Tuning edge-swap penalties**
**Adding endpoint classifiers**

**Refining edge-case movement gates**
**Tuning movement thresholds**

**Indexing predicates for h2**
**Refining brick-targeting strategy**

**Re-deriving threshold signs**

**Preparing feature weights**
**Estimating implementation size**

**Preparing W1 initialization**
**Preparing trail initialization**

**Configuring W2 weights**

**Setting action weights**
**Increasing mandatory weights**

**Checking paddle prediction**

**Refining upward centering**
**Adjusting the upward target band**

**Preparing weight assignments**

**Initializing paddle-channel weights**
**Configuring bias values**

**Verifying transition thresholds**
**Checking h2 edge bonuses**

**Initializing output weights**