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add notes on parameter tuning

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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Nikolaj Bjorner 2025-08-12 14:51:11 -07:00
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PARALLEL_PROJECT_NOTES.md
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@ -137,10 +137,16 @@ if a parameter mutation step results in an improvement, and decremented if a mut
$P = \{ (p_1, v_1, \{ (r_{11}, m_{11}), \ldots, (r_{1k_1}, m_{1k_1}) \}), \ldots, (p_n, v_n, \{ (r_{n1}, m_{n1}), \ldots, (r_{nk_n}, m_{nk_n})\}) \}$.
The initial values of reward functions is fixed (to 1) and the initial values of parameters are the defaults.
The batch manager maintains a set of candidate parameters $CP = \{ (P_1, r_1), \ldots, (P_n, r_n) \}$.
A worker thread picks up a parameter $P_i$ from $CP$ from the batch manager.
It picks one or more parameter settings within $P_i$ whose mutation function have non-zero reward functions and applies a mutation.
It then runs with a bounded set of cubes.
It measures the reward for the new parameter setting based in number of cubes, cube depth, number of timeouts, and completions with number of conflicts.
If the new reward is an improvement over $(P_i, r_i)$ it inserts the new parameter setting $(P_i', r_i')$ into the batch manager.
The batch manager discards the worst parameter settings keeping the top $K$ ($K = 5$) parameter settings.
* The batch manager maintains a set of candidate parameters $CP = \{ (P_1, r_1), \ldots, (P_n, r_n) \}$.
* A worker thread picks up a parameter $P_i$ from $CP$ from the batch manager.
* It picks one or more parameter settings within $P_i$ whose mutation function have non-zero reward functions and applies a mutation.
* It then runs with a bounded set of cubes.
* It measures the reward for the new parameter setting based in number of cubes, cube depth, number of timeouts, and completions with number of conflicts.
* If the new reward is an improvement over $(P_i, r_i)$ it inserts the new parameter setting $(P_i', r_i')$ into the batch manager.
* The batch manager discards the worst parameter settings keeping the top $K$ ($K = 5$) parameter settings.
When picking among mutation steps with reward functions use a weighted sampling algorithm.
Weighted sampling works as follows: You are given a set of items with weights $(i_1, w_1), \ldots, (i_k, w_k)$.
Add $w = \sum_j w_j$. Pick a random number $w_0$ in the range $0\ldots w$.
Then you pick item $i_n$ such that $n$ is the smallest index with $\sum_{j = 1}^n w_j \geq w_0$.