[Feat] grid cardinality auto switch

[VincentG1234]

Summary

This PR adds grid cardinality calculation and implements smart sampler selection logic to automatically switch between optimization strategies based on the study configuration.

Changes

New: Grid Cardinality Calculator (auto_tune_vllm/utils/grid_cardinality.py)

• Computes the total number of parameter combinations in the search space
• Supports all parameter types: ListParameter, RangeParameter, BooleanParameter

Smart Sampler Auto-Switching (auto_tune_vllm/cli/main.py)

Case 1: n_trials >= grid_cardinality

• Action: Switch to sampler="grid" and set n_trials = cardinality
• Why: Grid search explores all combinations exhaustively
• User benefit: No wasted trials on duplicate parameter combinations

Case 2: n_trials <= n_startup_trials

• Action: Switch to sampler="random" and ignore n_startup_trials
• Why: TPE's startup phase is meaningless when we can't even complete it
• User benefit: Immediate optimization without waiting for random startup

CLI Enhancement

• Grid cardinality is now displayed in the validate command output
• Clear warning messages inform users when auto-switching occurs

Example Behavior

study_config.yaml with small search space
parameters:
tensor_parallel_size:
type: list
options: [1, 2] # 2 values
dtype:
type: list
options: [float16, bfloat16] # 2 values
→ Grid cardinality = 2 × 2 = 4

• If user requests --trials 10 (> 4) → Warning: n_trials (10) exceeds grid cardinality (4). Search set to grid mode with n_trials = 4.

• If user requests --trials 5 with n_startup_trials=10 → Warning: n_trials (5) <= n_startup_trials (10). Search set to random mode; n_startup_trials ignored.