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DD2380 HT24 (AIHT24_2) Q5: Decision making

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Which of the following algorithms is used to find a policy?

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A.Value iteration

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The question asks: Which of the following algorithms is used to find a policy? Option: Value iteration To understand why this is the focus, recall that in the context of Markov Decision Processes (MDPs), a policy defines the action......Login to view full explanation

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表: Gridworld MDP 2 5 1 S -5 A B C 图：转换函数 0.8 ^ 0.1 <- | -> 0.1 查看表 (Gridworld MDP) 和图（转移函数）。Gridworld MDP 以讲座中讨论的方式运行。状态是网格方块，由其行（A、B 或 C）和列（1 或 2）值标识，如表中所示。智能体的初始状态始终是 (A,1)，用字母 S 标记。有两个终止目标状态：奖励为 -5 的 (B,1) 和奖励为 +5 的 (B,2)。非终止状态下奖励为 0。（在智能体执行下一个动作之前，收到状态奖励。）转移函数（参见图）使得智能体以 0.8 的概率发生预期的移动（上、下、左或右）。智能体最终处于与预期方向垂直的状态之一的概率各为 0.1。如果与墙壁发生碰撞，智能体将保持状态不变，并且漂移概率将添加到保持相同状态的概率中。假设 V 1 1(A,1) = 0, V 1 1C,1) = 0, V 1 1(C,2) = 4, V 1 1(A,2) = 4, V 1 1(B,1) = -5，V 1 1(B,2) = +5 根据这些信息，状态 (A,1) 使用折扣因子 0.5 进行的第二轮值迭代 (V2) 更新是什么？ Review Table: Gridworld MDP and Figure: Transition Function. The gridworld MDP operates like the one discussed in lecture. The states are grid squares, identified by their column (A, B, or C) and row (1 or 2) values, as presented in the table. The agent always starts in state (A,1), marked with the letter S. There are two terminal goal states: (B,1) with reward -5, and (B,2) with reward +5. Rewards are 0 in non-terminal states. (The reward for a state is received before the agent applies the next action.) The transition function in Figure: Transition Function is such that the intended agent movement (Up, Down, Left, or Right) happens with probability 0.8. The probability that the agent ends up in one of the states perpendicular to the intended direction is 0.1 each. If a collision with a wall happens, the agent stays in the same state, and the drift probability is added to the probability of remaining in the same state. Assume that V 1 (A,1) = 0, V 1 C,1) = 0, V 1 (C,2) = 4, V 1 (A,2) = 4, V 1 (B,1) = -5, and V 1 (B,2) = +5. Given this information, what is the second round of value iteration (V 2 ) update for state (A,1) with a discount of 0.5?

有一个 2×3 网格表示我们的 MDP 世界。从左到右的列分别标记为 A、B、C。从下到上的行分别标记为 1、2。第 1 行 A 列包含字母“S”。第 2 行 A 列包含数字“-1”。第 2 行 C 列包含数字“+1”。表：Gridworld MDP。 A 2-by-3 grid representing our MDP world. Moving left to right, the columns are labeled A, B, C. Moving bottom to top, rows are labeled 1, 2. Row 1, Column A contains a letter "S". Row 2, Column A contains the number "-1". Row 2, column C contains the number "+1". Table: Gridworld MDP. 图：转移函数（Artificial intelligence - a modern approach，Russell, Stuart J 和 Norvig, Peter）。查看表 (Gridworld MDP) 和图（转移函数）。Gridworld MDP 以讲座中讨论的方式运行。状态是网格方块，由其列（A、B 或 C）和行（1 或 2）值标识，如表中所示。智能体的初始状态始终是 (A,1)，用字母 S 标记。有两个终止目标状态：奖励为 +1 的 (C,2) 和奖励为 -1 的 (A,2)。非终止状态下奖励为 0。（在智能体执行下一个动作之前，收到状态奖励。）转移函数（图）使得智能体以 0.8 的概率发生预期的移动（上、下、左或右）。智能体最终处于与预期方向垂直的状态之一的概率各为 0.1。如果与墙壁发生碰撞，智能体将保持状态不变，并且漂移概率将添加到保持相同状态的概率中。假设对于每个非终止状态，V1 = 0。根据这些信息，状态 (B,2) 使用折扣因子 0.9 进行的第二轮值迭代 (V2) 更新是什么？ Figure: Transition Function ( Artificial intelligence — a modern approach, Russell, Stuart J and Norvig, Peter). Review the table (Gridworld MDP) and the figure (Transition Function). The gridworld MDP operates like the one discussed in lecture. The states are grid squares, identified by their column (A, B, or C) and row (1 or 2) values, as presented in the table. The agent always starts in state (A,1), marked with the letter S. There are two terminal goal states: (C,2) with reward +1, and (A,2) with reward -1. Rewards are 0 in non-terminal states. (The reward for a state is received before the agent applies the next action.) The transition function (Figure) is such that the intended agent movement (Up, Down, Left, or Right) happens with probability 0.8. The probability that the agent ends up in one of the states perpendicular to the intended direction is 0.1 each. If a collision with a wall happens, the agent stays in the same state, and the drift probability is added to the probability of remaining in the same state. Assume that V11 = 0 for every non-terminal state. Given this information, what is the second round of value iteration (V22) update for state (B,2) with a discount of 0.9?

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