Add fractional batch size search for MaxText estimator

[NuojCheng]

Description

Start with a short description of what the PR does and how this is a change from
the past.

The rest of the description includes relevant details and context, examples:

• why is this change being made,
• the problem being solved and any relevant context,
• why this is a good solution,
• some information about the specific implementation,
• shortcomings of the solution and possible future improvements.

If the change fixes a bug or a Github issue, please include a link, e.g.,:
FIXES: b/123456
FIXES: #123456

Notice 1: Once all tests pass, the "pull ready" label will automatically be assigned.
This label is used for administrative purposes. Please do not add it manually.

Notice 2: For external contributions, our settings currently require an approval from a MaxText maintainer to trigger CI tests.

Tests

Test 1: search both batch sizes and remat policies (llama3.1-405b on tpu7x-1024)

Command

python -m MaxText.estimator \
MaxText/configs/base.yml \
compile_topology=tpu7x-1024 \
compile_topology_num_slices=1 \
model_name=llama3.1-405b \
max_target_length=32768 \
ici_context_parallelism=8 \
ici_fsdp_parallelism=-1 \
log_config=False \
write_estimator_result=False

Output recommendation:

Search completed in 971.74 seconds.
  - Found valid combo (not saved to file): pdb=0.25, policy={'mlpwo': 'remat', 'context': 'remat', 'mlpwi_0': 'remat', 'mlpwi_1': 'remat', 'query_proj': 'remat', 'out_proj': 'remat', 'key_proj': 'remat', 'value_proj': 'remat'}
  - Found valid combo (not saved to file): pdb=0.125, policy={'mlpwo': 'offload', 'context': 'offload', 'mlpwi_0': 'offload', 'mlpwi_1': 'offload', 'query_proj': 'device', 'out_proj': 'device', 'key_proj': 'device', 'value_proj': 'device'}
  - Found valid combo (not saved to file): pdb=0.125, policy={'mlpwo': 'remat', 'context': 'remat', 'mlpwi_0': 'remat', 'mlpwi_1': 'offload', 'query_proj': 'offload', 'out_proj': 'offload', 'key_proj': 'offload', 'value_proj': 'offload'}
  - Found valid combo (not saved to file): pdb=0.25, policy={'mlpwo': 'remat', 'context': 'remat', 'mlpwi_0': 'remat', 'mlpwi_1': 'remat', 'query_proj': 'offload', 'out_proj': 'offload', 'key_proj': 'offload', 'value_proj': 'offload'}
  - Found valid combo (not saved to file): pdb=0.25, policy={'mlpwo': 'remat', 'context': 'remat', 'mlpwi_0': 'remat', 'mlpwi_1': 'remat', 'query_proj': 'remat', 'out_proj': 'offload', 'key_proj': 'offload', 'value_proj': 'offload'}
  - Found valid combo (not saved to file): pdb=0.25, policy={'mlpwo': 'remat', 'context': 'remat', 'mlpwi_0': 'remat', 'mlpwi_1': 'remat', 'query_proj': 'remat', 'out_proj': 'remat', 'key_proj': 'offload', 'value_proj': 'offload'}
  - Found valid combo (not saved to file): pdb=0.25, policy={'mlpwo': 'remat', 'context': 'remat', 'mlpwi_0': 'remat', 'mlpwi_1': 'remat', 'query_proj': 'remat', 'out_proj': 'remat', 'key_proj': 'remat', 'value_proj': 'offload'}
  - Found valid combo (not saved to file): pdb=0.25, policy={'mlpwo': 'remat', 'context': 'remat', 'mlpwi_0': 'remat', 'mlpwi_1': 'remat', 'query_proj': 'remat', 'out_proj': 'remat', 'key_proj': 'remat', 'value_proj': 'remat'}
Done.

Full output: log

Test 2: search both batch size and remat policies only (deepseek3-671b on v5p-1024)

python3 -m MaxText.estimator MaxText/configs/base.yml \
model_name=deepseek3-671b \
compile_topology=v5p-1024 \
compile_topology_num_slices=1 \
ici_fsdp_parallelism=64 \
ici_expert_parallelism=8 \
dtype=bfloat16 \
weight_dtype=float32 \
scan_layers=True \
sparse_matmul=True \
use_custom_sort_vjp=False \
use_tokamax_splash=True \
use_tokamax_gmm=True \
sa_use_fused_bwd_kernel=False \
max_target_length=8192 \
sa_block_q=1024 \
sa_block_kv=1024 \
sa_block_kv_compute=1024 \
sa_block_q_dkv=1024 \
sa_block_kv_dkv=1024 \
sa_block_kv_dkv_compute=1024 \
sa_block_q_dq=1024 \
sa_block_kv_dq=1024 \
log_config=False \
write_estimator_result=False

Checklist

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• I have performed a self-review of my code. For an optional AI review, add the gemini-review label.
• I have necessary comments in my code, particularly in hard-to-understand areas.
• I have run end-to-end tests tests and provided workload links above if applicable.
• I have made or will make corresponding changes to the doc if needed, including adding new documentation pages to the relevant Table of Contents (toctree directive) as explained in our documentation.

[codecov]

Codecov Report

❌ Patch coverage is 0% with 31 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/MaxText/estimator.py	0.00%	31 Missing ⚠️

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