Agent Conversation: anthropic/claude-opus-4.6

Model: anthropic/claude-opus-4.6
Total steps: 2
Messages: 5
UserStep 0

Task: optimization-convex-concave

RAIN Convex-Concave

Research Question

Can you improve gradient-norm convergence on the exact convex-concave benchmark instances used by the official RAIN repository for src/bilinear_func/exp_gnorm.m and src/delta_func/exp_gnorm.m?

What You Can Modify

Edit only the scaffold file RAIN/optimization_convex_concave/custom_strategy.py inside the editable block containing:

  1. init_state(problem, initial_z, seed, hyperparameters)
  2. step(state, oracle, problem, hyperparameters, max_sfo_calls)
  3. get_hyperparameters(problem_name, sigma)

The benchmark harness, problem definitions, update-noise model, official iteration counts, initializations, and metric computation are fixed.

Fixed Setup

  • Problems:
    • bilinear: the official scalar bilinear problem f(x, y) = x y with n = 900, tau = 0.1, z0 = [10, 10]^T, sigma = 0.001
    • delta_nu: the official (delta, nu) problem with d = 100, delta = 1e-2, nu = 5e-5, n = 6000, tau = 1, sigma = 0.02, and z0 ~ N(0, I) under the script's fixed RNG seed
  • The harness mirrors the official scripts' additive Gaussian update noise, not the earlier generalized SFO sweep variant
  • Evaluation uses the official per-problem iteration counts and the same gradient-norm quantities plotted by the scripts
  • Main metric: final_gradient_norm, the mean of the two official final gradient norms

Interface Notes

  • init_state(...) must preserve the provided starting point in state["z"]
  • step(...) should implement one official-style iteration of the chosen method
  • The oracle exposes deterministic gradients and fixed-scale Gaussian update noise so the update equations can match the MATLAB scripts directly
  • get_hyperparameters(...) should return the per-problem constants used by the method

Metrics

  • Lower is better
  • The harness prints:
    • STEP_METRICS problem=... iteration=... gradient_norm=...
    • RUN_METRICS problem=... final_gradient_norm=... auc_log_iteration_log_grad=...
    • FINAL_METRICS final_gradient_norm=...

Read-Only References

  • RAIN/README.md
  • RAIN/src/bilinear_func/exp_gnorm.m
  • RAIN/src/delta_func/exp_gnorm.m

These are the primary references. The task now follows those scripts directly rather than the earlier MLS-Bench-specific generalized variant.

RAIN/optimization_convex_concave/custom_strategy.py [EDITABLE — lines 24–75 only]

     1: """Editable strategy scaffold for the optimization-convex-concave MLS-Bench task."""
     2: 
     3: from __future__ import annotations
     4: 
     5: from typing import Any
     6: 
     7: import numpy as np
     8: 
     9: from fixed_benchmark import (
    10:     ProblemSpec,
    11:     StepOutput,
    12:     StochasticOracle,
    13:     as_vector,
    14:     make_step_output,
    15:     run_cli,
    16: )
    17: 
    18: 
    19: # =====================================================================
    20: # EDITABLE: init_state, step,
AssistantStep 1edit
Tool Input
1{
2  "op": "replace",
3  "filename": "RAIN/optimization_convex_concave/custom_strategy.py",
4  "start_line": 24,
5  "end_line": 75,
6  "content": "def init_state(\n    problem: ProblemSpec,\n    initial_z: np.ndarray,\n    seed: int,\n    hyperparameters: dict[str, Any],\n) -> dict[str, Any]:\n    \"\"\"Initialize with RAIN state plus previous gradient for optimistic updates.\"\"\"\n    z0 = as_vector(initial_z, expected_dim=2 * problem.dim)\n    return {\n        \"z\": z0,\n        \"step_index\": 0,\n        \"weight_sum\": 0.0,\n        \"weighted_flow_sum\": np.zeros_like(z0),\n        \"g_prev\": np.zeros_like(z0),\n    }\n\n\ndef step(\n    state: dict[str, Any],\n    oracle: StochasticOracle,\n    problem: ProblemSpec,\n    hyperparameters: dict[str, Any],\n    max_sfo_calls: int,\n) -> StepOutput:\n    \"\"\"Double Optimistic RAIN: two Popov-style sub-steps with RAIN anchoring.\n\n    Uses 2 gradient evals (same as EG) but performs 2 optimistic updates,\n    effectively doubling convergence progress per harness iteration.\n    \"\"\"\n    tau = float(hyperparameters[\"tau\"])\n    lam = float(hyperparameters[\"lambda\"])\n    gamma = float(hyperparameters[\"gamma\"])\n    dim2 = 2 * problem.dim\n    z = as_vector(state[\"z\"], expected_dim=dim2)\n    k = int(state.get(\"step_index\", 0))\n    ws = float(state.get(\"weight_sum\", 0.0))\n    wfs = as_vector(state.get(\"weighted_flow_sum\", np.zeros_like(z)), expected_dim=dim2)\n    gp = as_vector(state.get(\"g_prev\", np.zeros_like(z)), expected_dim=dim2)\n    # --- Sub-step 1: optimistic gradient + RAIN anchor ---\n    g1 = oracle.grad(z)\n    d1 = (2.0 * g1 - gp) if k > 0 else g1\n    z_mid = z - tau * d1 + tau * lam * (wfs - ws * z) + oracle.noise()\n    w1 = gamma * (1.0 + gamma) ** (2 * k + 1)\n    ws1, wfs1 = ws + w1, wfs + w1 * z_mid\n    # --- Sub-step 2: optimistic gradient + RAIN anchor ---\n    g2 = oracle.grad(z_mid)\n    d2 = 2.0 * g2 - g1\n    z_next = z_mid - tau * d2 + tau * lam * (wfs1 - ws1 * z_mid) + oracle.noise()\n    w2 = gamma * (1.0 + gamma) ** (2 * k + 2)\n    next_state = {\n        \"z\": z_next, \"step_index\": k + 1,\n        \"weight_sum\": ws1 + w2,\n        \"weighted_flow_sum\": wfs1 + w2 * z_next,\n        \"g_prev\": g2.copy(),\n    }\n    metric_iterate = z_next if problem.name == \"bilinear\" else z\n    return make_step_output(next_state, metric_iterate, 2)\n\n\ndef get_hyperparameters(problem_name: str, sigma: float) -> dict[str, Any]:\n    \"\"\"Per-problem hyperparameters; gamma halved to match 2x sub-step schedule.\"\"\"\n    if problem_name == \"bilinear\":\n        return {\"tau\": 0.1, \"lambda\": 0.1, \"gamma\": 0.0005}\n    if problem_name == \"delta_nu\":\n        return {\"tau\": 1.0, \"lambda\": 0.01, \"gamma\": 0.00005}\n    raise KeyError(f\"Unknown problem: {problem_name}\")\n\n\n"
7}
Tool ResultStep 1
OK: Replaced lines 24..75 with 68 line(s) in RAIN/optimization_convex_concave/custom_strategy.py. Editable range: 24–91.

[Current file: RAIN/optimization_convex_concave/custom_strategy.py | editable: 24–91 | total: 97 lines]
    21| # =====================================================================
    22| 
    23| 
    24  def init_state(
    25      problem: ProblemSpec,
    26      initial_z: np.ndarray,
    27      seed: int,
    28      hyperparameters: dict[str, Any],
    29  ) -> dict[str, Any]:
    30      """Initialize with RAIN state plus previous gradient for optimistic updates."""
    31      z0 = as_vector(initial_z, expected_dim=2 * problem.dim)
    32      return {
    33          "z": z0,
    34          "step_index": 0,
    35          "weight_sum": 0.0,
    36          "weighted_flow_sum": np.zeros_like(z0),
    37          "g_prev": np.zeros_like(z0),
    38      }
    39  
    40  
    41  def step(
    42      state: dict[str, Any],
    43      oracle: Stocha
AssistantStep 2test
Tool ResultStep 2
[Test #1] (2 tests remaining; call submit(n=1) to submit this result)

### default-noise (scripts/eval.sh)
Recent checkpoints:
STEP_METRICS problem=delta_nu iteration=10 sfo_calls=20 gradient_norm=0.130236
STEP_METRICS problem=delta_nu iteration=100 sfo_calls=200 gradient_norm=0.133842
STEP_METRICS problem=delta_nu iteration=500 sfo_calls=1000 gradient_norm=0.116722
STEP_METRICS problem=delta_nu iteration=1000 sfo_calls=2000 gradient_norm=0.073931
STEP_METRICS problem=delta_nu iteration=3000 sfo_calls=6000 gradient_norm=0.030908
STEP_METRICS problem=delta_nu iteration=6000 sfo_calls=12000 gradient_norm=0.022490

Recent runs:
RUN_METRICS problem=bilinear final_gradient_norm=0.011953 auc_log_iteration_log_grad=1.396392 total_sfo_calls=1800
RUN_METRICS problem=delta_nu final_gradient_norm=0.022490 auc_log_iteration_log_grad=-3.784652 total_sfo_calls=12000

Final metrics:
FINAL_METRICS final_gradient_norm=0.017221 score=-0.017221 auc_log_iteration_log_grad=-1.194130 bilinear_final_gradient