SSP-MMC
maimemo • Updated Apr 21, 2025
SSP: stochastic shortest path
MMC: minimize memorization cost
In traditional spaced repetition algorithms, reviews are endless. In this paper, we remove items from the review schedule once their stability reaches a certain threshold. This introduces a new problem to solve: how to design a review scheduling algorithm that minimizes the expected cost (such as time) of reviewing items.
- Symbols：
- - initial stability
- - target stability
- - result of review（recall = 1，forget = 0）
- - transition equation of stability
- - Calculate the next stability based on the current stability and the next review interval.
- - cost function of review
- - cost of recall
- - cost of forget
- - total cost of review
Given the random nature of stability transitions and the existence of a target stability threshold, this problem can be reformulated as a stochastic shortest path problem.
Bellman's equation:
Iteration equation:
Using this equation, we can obtain an iterative solution through dynamic programming. However, since is a continuous value, it's not ideal for recording states. To address this, we can discretize it.
