N-step Off-policy Sarsa.kt

@file:Suppress("NAME_SHADOWING")

package lab.mars.rl.algo.ntd

import lab.mars.rl.algo.V_from_Q
import lab.mars.rl.algo.`ε-greedy`
import lab.mars.rl.model.impl.mdp.IndexedAction
import lab.mars.rl.model.impl.mdp.IndexedMDP
import lab.mars.rl.model.impl.mdp.IndexedState
import lab.mars.rl.model.impl.mdp.OptimalSolution
import lab.mars.rl.model.isTerminal
import lab.mars.rl.model.log
import lab.mars.rl.util.buf.newBuf
import lab.mars.rl.util.log.debug
import lab.mars.rl.util.math.Π
import lab.mars.rl.util.math.Σ
import lab.mars.rl.util.tuples.tuple3
import org.apache.commons.math3.util.FastMath.min
import org.apache.commons.math3.util.FastMath.pow

fun IndexedMDP.`N-step off-policy sarsa`(
    n: Int,
    ε: Double,
    α: (IndexedState, IndexedAction) -> Double,
    episodes: Int): OptimalSolution {
  val b = equiprobablePolicy()
  val π = equiprobablePolicy()
  
  val Q = QFunc { 0.0 }
  val _R = newBuf<Double>(min(n, MAX_N))
  val _S = newBuf<IndexedState>(min(n, MAX_N))
  val _A = newBuf<IndexedAction>(min(n, MAX_N))
  
  for (episode in 1..episodes) {
    log.debug { "$episode/$episodes" }
    var n = n
    var T = Int.MAX_VALUE
    var t = 0
    var s = started()
    var a = b(s)
    _R.clear();_R.append(0.0)
    _S.clear();_S.append(s)
    _A.clear();_A.append(a)
    do {
      if (t >= n) {
        _R.removeFirst()
        _S.removeFirst()
        _A.removeFirst()
      }
      if (t < T) {
        val (s_next, reward) = a.sample()
        _R.append(reward)
        _S.append(s_next)
        s = s_next
        if (s.isTerminal) {
          T = t + 1
          val τ = t - n + 1
          if (τ < 0) n = T
        } else {
          a = b(s)
          _A.append(a)
        }
      }
      val τ = t - n + 1
      if (τ >= 0) {
        val ρ = Π(1..min(n - 1, T - 1 - τ)) { π[_S[it], _A[it]] / b[_S[it], _A[it]] }
        var G = Σ(1..min(n, T - τ)) { pow(γ, it - 1) * _R[it] }
        if (τ + n < T) G += pow(γ, n) * Q[_S[n], _A[n]]
        Q[_S[0], _A[0]] += α(_S[0], _A[0]) * ρ * (G - Q[_S[0], _A[0]])
        `ε-greedy`(_S[0], Q, π, ε)
      }
      t++
    } while (τ < T - 1)
    log.debug { "n=$n,T=$T" }
  }
  val V = VFunc { 0.0 }
  val result = tuple3(π, V, Q)
  V_from_Q(states, result)
  return result
}