For the traditional dynamic programming algorithms used for solving MDPs, which of the following statements holds true.

Question

BlackTom AI · Accepted Answer

When evaluating traditional dynamic programming approaches for MDPs, we need to consider what each algorithm does at each backup step.
Option 1: 'Neither Q-Iteration nor Value Iteration require a discrete action space.' In standard finite MDPs, both methods involve taking a maximum over possible actions at each state (for Q-Iteration, max over actions when updating Q; for Value Iteration, max over actions when updating V). If the action space were continuous, these maximizations could become intractable or require approximation, which means this statement is generally incorrect for the typical, discrete-action setting.
Option 2: 'V-Iteration requires a discrete action space but Q-Iteration does not.' This claim splits the requirements between the two methods. In classic DP with discrete states and actions, Value Iteration computes V(s) = max_a sum_{s'} P(s'|s,a)[R(s,a,s') + gamma V(s')], which involves maximizing over actions and thus relies on a discrete set of actions to evaluate the max. Q-Iteration updates Q(s,a) using Q(s,a) = R(s,a) + gamma sum_{s'} P(s'|s,a) max_{a'} Q(s',a'), which also requires maximizing over a' and therefore needs a discrete action set. So this option misstates the requirements for both methods.
Option 3: 'Both Q-Iteration and Value iteration require a discrete action space.' This matches the standard DP setting: to perform the max over actions at each state, the action space must be discrete so the maximum is well-defined and computable. If actions were continuous, these backups would require solving a continuous optimization at each step, which is not part of the traditional discrete-action DP formulation.
Option 4: 'Q-Iteration requires a discrete action space but Value Iteration does not.' Similar to Option 2, this incorrectly separates the two methods. Value Iteration also hinges on taking a maximization over actions at each state, so it likewise presumes a discrete action set to keep the problem finite and tractable in the classical DP framework.
In summary, the core feature of both algorithms is the need to evaluate a maximum over the available actions at each state, which is straightforward when actions are discrete but becomes problematic or undefined for continuous action spaces without additional optimization machinery. The reasoning for each incorrect option highlights the specific mismatch with the standard discrete-action DP setup and clarifies why the correct choice aligns with Option 3.

For the traditional dynamic programming algorithms used for solving MDPs, which of the following statements holds true. 单项选择题

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