[cuda] fix unweighted percentile formula (L1 & quantile leaf renewal)

[maxwbuckley]

Summary

PercentileDevice in include/LightGBM/cuda/cuda_algorithms.hpp — used by the CUDA leaf-renewal kernels for regression_l1 and quantile objectives — computed the percentile position against len instead of len - 1, and indexed it 0-based instead of CPU's 1-based-with-+1 convention.

For alpha = 0.5 (median), this means CUDA returned:

len	CPU returns (correct)	CUDA before fix
even (e.g. 4)	avg(sorted[1], sorted[2]) — actual median	sorted[1] — biased toward upper
odd (e.g. 5)	sorted[2] — actual median	avg(sorted[1], sorted[2]) — biased toward upper

(sorted[] is descending here because PercentileDevice is called with ASCENDING=false.)

CPU PercentileFun (src/objective/regression_objective.hpp:28-29):

const double float_pos = static_cast<double>(cnt_data - 1) * (1.0 - alpha);
const data_size_t pos = static_cast<data_size_t>(float_pos) + 1;
...
const double bias = float_pos - (pos - 1);

This matches the standard Type-7 interpolated quantile — the same formula numpy.median and R's quantile() use by default.

Change

-    const double float_pos = (1.0f - alpha) * len;
-    const INDEX_T pos = static_cast<INDEX_T>(float_pos);
+    const double float_pos = (1.0 - alpha) * static_cast<double>(len - 1);
+    const INDEX_T pos = static_cast<INDEX_T>(float_pos) + 1;
     ...
-      const double bias = float_pos - pos;
+      const double bias = float_pos - static_cast<double>(pos - 1);

Reproducer (before fix)

[cuda]  num_leaves=7  (regression_l1)
  leaf 0: n=  7  np.median=-0.032  cuda=+0.529  delta=+0.561
  leaf 1: n= 72  np.median=-2.110  cuda=-1.763  delta=+0.347
  leaf 2: n= 23  np.median=+1.923  cuda=+2.221  delta=+0.298
  leaf 3: n=  9  np.median=-1.104  cuda=-0.791  delta=+0.313
  leaf 4: n= 10  np.median=+1.156  cuda=+1.703  delta=+0.547
  ...

(CPU's column matched np.median to FP epsilon throughout.)

Verification (after fix)

With learning_rate=1.0 to strip away shrinkage:

[cpu]   leaf 0: n=  7  np.median=-0.41937  raw=-0.41937  delta=-0.000000
[cuda]  leaf 0: n=  7  np.median=-0.41937  raw=-0.41937  delta=-0.000000
... every leaf matches ...

[cpu]   leaf 0: n=  6  np.quantile(0.7)=+0.806  raw=+0.806  delta=-0.000000
[cuda]  leaf 0: n=  6  np.quantile(0.7)=+0.806  raw=+0.806  delta=-0.000000
... every leaf matches ...

Parity-benchmark impact (scratch/cpu_cuda_parity.py from PR #4):

	before	after
reg_l1 max|Δ| raw_score	0.40	0.25
reg_quantile max|Δ| raw_score	0.58	0.54

For quantile, the test sweep additionally now produces identical leaf populations on both devices for alpha=0.7. For L1 there is a residual structural divergence (CPU and CUDA pick slightly different splits even on round 1 with identical gradients) that will be investigated separately — this PR fixes only the leaf-value calculation.

Scope notes

• The weighted-percentile path in PercentileDevice uses different conventions on CPU vs CUDA (ascending vs descending sort, alpha vs 1-alpha threshold) and is left untouched. None of the L1/quantile defaults exercise it.
• PercentileDevice is only called from cuda_regression_objective.cu (L1 and quantile renewal kernels). No other call sites in the tree learner depend on the old behavior.

Test plan

• scratch/probe_l1_median.py — every CUDA leaf now matches np.median to FP epsilon
• scratch/probe_quantile.py — every CUDA leaf now matches np.quantile(α=0.7) to FP epsilon
• Parity sweep — reg_l1 and reg_quantile both improved
• Weighted L1 / weighted quantile (unchanged path) — not yet tested

🤖 Generated with Claude Code

[BelixRogner]

Thanks Max, and Claude Code. The fix is precise — formula matches CPU's PercentileFun and numpy.median / R's Type-7 default. The three-tier test coverage (sweep over seeds, sweep over alphas, then explicit small even/odd cases that target the exact failure mode) is exactly the right shape for a numerical regression.

One small ask before merge: the new tests use os.environ.get("LIGHTGBM_TEST_CUDA", "0") != "1" for the CUDA gate, but the rest of the suite (including the test you added for PR #2 that's already merged) uses getenv("TASK", "") != "cuda". Could you align to the existing TASK=cuda convention so we don't need two env vars to run the full CUDA test suite? Same applies to PRs #7, #8, #9, #10 — easiest to do all at once.

Merging once that's in.

[maxwbuckley]

Switched to TASK=cuda to match the test_engine.py convention — pushed as 0cb8feb6. Same change applied on #7, #8, #9, #10.