A Lookup Table Design Method: Achieving O(1)-Query Complexity and No Memory Waste
摘要
When solving complex Markov Decision Processes (MDPs), the state value function can be represented by a parameterized function or a lookup table. Parameterized functions are space-efficient but computationally complex, while lookup tables are efficient but struggle with large state spaces, leading to memory waste or high query complexity. This study proposes a lookup table design with O(1) query complexity and no memory waste for complex MDPs commonly found in dynamic vehicle routing problems. We define a state key as a numerical triple and design two 3D arrays. Though initially memory-wasteful, we apply operations like mirroring, rotation, and translation to remove unused memory while maintaining O(1) query complexity. Our contributions are: (1) making state aggregation optional in certain MDPs, and (2) efficiently managing memory for querying complex data. An illustrative example is used throughout to enhance clarity.