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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:

init_state(problem, initial_z, seed, hyperparameters)
step(state, oracle, problem, hyperparameters, max_sfo_calls)
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  "end_line": 67,
5  "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    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    }\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    tau = float(hyperparameters[\"tau\"])\n    lam = float(hyperparameters[\"lambda\"])\n    gamma = float(hyperparameters[\"gamma\"])\n    z = as_vector(state[\"z\"], expected_dim=2 * problem.dim)\n    step_index = int(state.get(\"step_index\", 0))\n    weight_sum = float(state.get(\"weight_sum\", 0.0))\n    weighted_flow_sum = as_vector(state.get(\"weighted_flow_sum\", np.zeros_like(z)), expected_dim=2 * problem.dim)\n\n    g = oracle.grad(z)\n    anchor_z = tau * lam * (weighted_flow_sum - weight_sum * z)\n    w = z - tau * g + anchor_z + oracle.noise()\n    gw = oracle.grad(w)\n    anchor_w = tau * lam * (weighted_flow_sum - weight_sum * w)\n    z_next = z - tau * gw + anchor_w + oracle.noise()\n\n    current_weight = gamma * (1.0 + gamma) ** (step_index + 1)\n    next_state = {\n        \"z\": z_next,\n        \"step_index\": step_index + 1,\n        \"weight_sum\": weight_sum + current_weight,\n        \"weighted_flow_sum\": weighted_flow_sum + current_weight * z_next,\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    if problem_name == \"bilinear\":\n        return {\"tau\": 0.1, \"lambda\": 0.1, \"gamma\": 0.001}\n    if problem_name == \"delta_nu\":\n        return {\"tau\": 1.0, \"lambda\": 0.01, \"gamma\": 0.0001}\n    raise KeyError(f\"Unknown problem: {problem_name}\")",
6  "start_line": 24
7}

Tool ResultStep 1

OK: Replaced lines 24..67 with 54 line(s) in RAIN/optimization_convex_concave/custom_strategy.py. Editable range: 24–85.

[Current file: RAIN/optimization_convex_concave/custom_strategy.py | editable: 24–85 | total: 91 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      z0 = as_vector(initial_z, expected_dim=2 * problem.dim)
    31      return {
    32          "z": z0,
    33          "step_index": 0,
    34          "weight_sum": 0.0,
    35          "weighted_flow_sum": np.zeros_like(z0),
    36      }
    37  
    38  
    39  def step(
    40      state: dict[str, Any],
    41      oracle: StochasticOracle,
    42      problem: ProblemSpec,
    43      hyperparameters: dict[str, Any],
    44      max_sfo_calls: int,
    45  ) -> S

AssistantStep 2test

Tool ResultStep 2

[Test #1] (2 tests remaining; call submit(n=1) to submit this result)


## Seed 42

### default-noise (scripts/eval.sh)
Recent checkpoints:
STEP_METRICS problem=delta_nu iteration=10 sfo_calls=20 gradient_norm=0.130368
STEP_METRICS problem=delta_nu iteration=100 sfo_calls=200 gradient_norm=0.131880
STEP_METRICS problem=delta_nu iteration=500 sfo_calls=1000 gradient_norm=0.121082
STEP_METRICS problem=delta_nu iteration=1000 sfo_calls=2000 gradient_norm=0.094685
STEP_METRICS problem=delta_nu iteration=3000 sfo_calls=6000 gradient_norm=0.034590
STEP_METRICS problem=delta_nu iteration=6000 sfo_calls=12000 gradient_norm=0.022665

Recent runs:
RUN_METRICS problem=bilinear final_gradient_norm=0.020523 auc_log_iteration_log_grad=2.147154 total_sfo_calls=1800
RUN_METRICS problem=delta_nu final_gradient_norm=0.022665 auc_log_iteration_log_grad=-3.741447 total_sfo_calls=12000

Final metrics:
FINAL_METRICS final_gradient_norm=0.021594 score=-0.021594 auc_log_iteration_log_grad=-0.797146 bilinear_f

AssistantStep 3undo

Tool ResultStep 3

Undo complete:
Restored: RAIN/optimization_convex_concave/custom_strategy.py

AssistantStep 4edit

Tool Input

1{
2  "start_line": 24,
3  "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    z0 = as_vector(initial_z, expected_dim=2 * problem.dim)\n    return {\n        \"z\": z0,\n        \"sum_z\": z0.copy(),\n        \"step_index\": 0,\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    tau = float(hyperparameters[\"tau\"])\n    z = as_vector(state[\"z\"], expected_dim=2 * problem.dim)\n    sum_z = as_vector(state[\"sum_z\"], expected_dim=2 * problem.dim)\n    step_index = int(state.get(\"step_index\", 0))\n\n    g = oracle.grad(z)\n    w = z - tau * g + oracle.noise()\n    gw = oracle.grad(w)\n    z_next = z - tau * gw + oracle.noise()\n    \n    new_sum = sum_z + z_next\n    avg_z = new_sum / (step_index + 2)\n    \n    metric_iterate = avg_z\n    return make_step_output(\n        {\"z\": z_next, \"sum_z\": new_sum, \"step_index\": step_index + 1},\n        metric_iterate,\n        2,\n    )\n\n\ndef get_hyperparameters(problem_name: str, sigma: float) -> dict[str, Any]:\n    if problem_name == \"bilinear\":\n        return {\"tau\": 0.1}\n    if problem_name == \"delta_nu\":\n        return {\"tau\": 1.0}\n    raise KeyError(f\"Unknown problem: {problem_name}\")",
4  "op": "replace",
5  "filename": "RAIN/optimization_convex_concave/custom_strategy.py",
6  "end_line": 67
7}

Tool ResultStep 4

OK: Replaced lines 24..67 with 48 line(s) in RAIN/optimization_convex_concave/custom_strategy.py. Editable range: 24–79.

[Current file: RAIN/optimization_convex_concave/custom_strategy.py | editable: 24–79 | total: 85 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      z0 = as_vector(initial_z, expected_dim=2 * problem.dim)
    31      return {
    32          "z": z0,
    33          "sum_z": z0.copy(),
    34          "step_index": 0,
    35      }
    36  
    37  
    38  def step(
    39      state: dict[str, Any],
    40      oracle: StochasticOracle,
    41      problem: ProblemSpec,
    42      hyperparameters: dict[str, Any],
    43      max_sfo_calls: int,
    44  ) -> StepOutput:
    45      tau = float(hyperparameters["tau

AssistantStep 5test

Tool ResultStep 5

[Test #2] (1 test remaining; call submit(n=2) to submit this result)

### default-noise (scripts/eval.sh)
Recent checkpoints:
STEP_METRICS problem=delta_nu iteration=10 sfo_calls=20 gradient_norm=0.130602
STEP_METRICS problem=delta_nu iteration=100 sfo_calls=200 gradient_norm=0.125150
STEP_METRICS problem=delta_nu iteration=500 sfo_calls=1000 gradient_norm=0.033890
STEP_METRICS problem=delta_nu iteration=1000 sfo_calls=2000 gradient_norm=0.026871
STEP_METRICS problem=delta_nu iteration=3000 sfo_calls=6000 gradient_norm=0.008889
STEP_METRICS problem=delta_nu iteration=6000 sfo_calls=12000 gradient_norm=0.005934

Recent runs:
RUN_METRICS problem=bilinear final_gradient_norm=0.158276 auc_log_iteration_log_grad=1.552034 total_sfo_calls=1800
RUN_METRICS problem=delta_nu final_gradient_norm=0.005934 auc_log_iteration_log_grad=-4.543917 total_sfo_calls=12000

Final metrics:
FINAL_METRICS final_gradient_norm=0.082105 score=-0.082105 auc_log_iteration_log_grad=-1.495942 bilinear_final_gradient_

AssistantStep 6edit

Tool Input

1{
2  "op": "replace",
3  "start_line": 24,
4  "end_line": 71,
5  "filename": "RAIN/optimization_convex_concave/custom_strategy.py",
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    z0 = as_vector(initial_z, expected_dim=2 * problem.dim)\n    return {\n        \"z\": z0,\n        \"anchor_z\": z0.copy(),\n        \"step_index\": 0,\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    tau = float(hyperparameters[\"tau\"])\n    z = as_vector(state[\"z\"], expected_dim=2 * problem.dim)\n    anchor_z = as_vector(state[\"anchor_z\"], expected_dim=2 * problem.dim)\n    step_index = int(state.get(\"step_index\", 0))\n    coeff = 1.0 / (step_index + 3.0)\n\n    g = oracle.grad(z)\n    w = z - tau * g + coeff * (anchor_z - z) + oracle.noise()\n    gw = oracle.grad(w)\n    z_next = z - tau * gw + coeff * (anchor_z - z) + oracle.noise()\n    \n    metric_iterate = z_next if problem.name == \"bilinear\" else z\n    return make_step_output(\n        {\"z\": z_next, \"anchor_z\": anchor_z, \"step_index\": step_index + 1},\n        metric_iterate,\n        2,\n    )\n\ndef get_hyperparameters(problem_name: str, sigma: float) -> dict[str, Any]:\n    if problem_name == \"bilinear\":\n        return {\"tau\": 0.1}\n    if problem_name == \"delta_nu\":\n        return {\"tau\": 1.0}\n    raise KeyError(f\"Unknown problem: {problem_name}\")"
7}

Tool ResultStep 6

OK: Replaced lines 24..71 with 44 line(s) in RAIN/optimization_convex_concave/custom_strategy.py. Editable range: 24–75.

[Current file: RAIN/optimization_convex_concave/custom_strategy.py | editable: 24–75 | total: 81 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      z0 = as_vector(initial_z, expected_dim=2 * problem.dim)
    31      return {
    32          "z": z0,
    33          "anchor_z": z0.copy(),
    34          "step_index": 0,
    35      }
    36  
    37  def step(
    38      state: dict[str, Any],
    39      oracle: StochasticOracle,
    40      problem: ProblemSpec,
    41      hyperparameters: dict[str, Any],
    42      max_sfo_calls: int,
    43  ) -> StepOutput:
    44      tau = float(hyperparameters["tau"])

AssistantStep 7test

Tool ResultStep 7

[Test #3] (0 tests remaining)


## Seed 42

### default-noise (scripts/eval.sh)
Recent checkpoints:
STEP_METRICS problem=delta_nu iteration=10 sfo_calls=20 gradient_norm=0.130810
STEP_METRICS problem=delta_nu iteration=100 sfo_calls=200 gradient_norm=0.125678
STEP_METRICS problem=delta_nu iteration=500 sfo_calls=1000 gradient_norm=0.047183
STEP_METRICS problem=delta_nu iteration=1000 sfo_calls=2000 gradient_norm=0.052869
STEP_METRICS problem=delta_nu iteration=3000 sfo_calls=6000 gradient_norm=0.082902
STEP_METRICS problem=delta_nu iteration=6000 sfo_calls=12000 gradient_norm=0.110307

Recent runs:
RUN_METRICS problem=bilinear final_gradient_norm=0.160590 auc_log_iteration_log_grad=1.543492 total_sfo_calls=1800
RUN_METRICS problem=delta_nu final_gradient_norm=0.110307 auc_log_iteration_log_grad=-3.757965 total_sfo_calls=12000

Final metrics:
FINAL_METRICS final_gradient_norm=0.135449 score=-0.135449 auc_log_iteration_log_grad=-1.107236 bilinear_final_gradient_norm=0.160590 delta_nu_fin

AssistantStep 1edit

Tool Input

1{
2  "op": "replace",
3  "start_line": 24,
4  "end_line": 69,
5  "filename": "RAIN/optimization_convex_concave/custom_strategy.py",
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    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    }\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    tau = float(hyperparameters[\"tau\"])\n    lam = float(hyperparameters[\"lambda\"])\n    gamma = float(hyperparameters[\"gamma\"])\n    z = as_vector(state[\"z\"], expected_dim=2 * problem.dim)\n    step_index = int(state.get(\"step_index\", 0))\n    weight_sum = float(state.get(\"weight_sum\", 0.0))\n    weighted_flow_sum = as_vector(state.get(\"weighted_flow_sum\", np.zeros_like(z)), expected_dim=2 * problem.dim)\n\n    # Proximal standard update\n    g = oracle.grad(z)\n    denom = 1.0 + tau * lam * weight_sum\n    w = (z - tau * g + tau * lam * weighted_flow_sum) / denom + oracle.noise()\n    \n    gw = oracle.grad(w)\n    z_next = (z - tau * gw + tau * lam * weighted_flow_sum) / denom + oracle.noise()\n\n    current_weight = gamma * (1.0 + gamma) ** (step_index + 1)\n    next_state = {\n        \"z\": z_next,\n        \"step_index\": step_index + 1,\n        \"weight_sum\": weight_sum + current_weight,\n        \"weighted_flow_sum\": weighted_flow_sum + current_weight * z_next,\n    }\n    metric_iterate = z_next if problem.name == \"bilinear\" else z\n    return make_step_output(next_state, metric_iterate, 2)\n\ndef get_hyperparameters(problem_name: str, sigma: float) -> dict[str, Any]:\n    if problem_name == \"bilinear\":\n        return {\"tau\": 0.1, \"lambda\": 0.1, \"gamma\": 0.001}\n    if problem_name == \"delta_nu\":\n        return {\"tau\": 1.0, \"lambda\": 0.01, \"gamma\": 0.0001}\n    raise KeyError(f\"Unknown problem: {problem_name}\")"
7}

Tool ResultStep 1

OK: Replaced lines 24..69 with 53 line(s) in RAIN/optimization_convex_concave/custom_strategy.py. Editable range: 24–82.

[Current file: RAIN/optimization_convex_concave/custom_strategy.py | editable: 24–82 | total: 88 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      z0 = as_vector(initial_z, expected_dim=2 * problem.dim)
    31      return {
    32          "z": z0,
    33          "step_index": 0,
    34          "weight_sum": 0.0,
    35          "weighted_flow_sum": np.zeros_like(z0),
    36      }
    37  
    38  def step(
    39      state: dict[str, Any],
    40      oracle: StochasticOracle,
    41      problem: ProblemSpec,
    42      hyperparameters: dict[str, Any],
    43      max_sfo_calls: int,
    44  ) -> StepOutput

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=0.130368
STEP_METRICS problem=delta_nu iteration=100 sfo_calls=200 gradient_norm=0.131880
STEP_METRICS problem=delta_nu iteration=500 sfo_calls=1000 gradient_norm=0.121082
STEP_METRICS problem=delta_nu iteration=1000 sfo_calls=2000 gradient_norm=0.094693
STEP_METRICS problem=delta_nu iteration=3000 sfo_calls=6000 gradient_norm=0.034595
STEP_METRICS problem=delta_nu iteration=6000 sfo_calls=12000 gradient_norm=0.022663

Recent runs:
RUN_METRICS problem=bilinear final_gradient_norm=0.020445 auc_log_iteration_log_grad=2.152654 total_sfo_calls=1800
RUN_METRICS problem=delta_nu final_gradient_norm=0.022663 auc_log_iteration_log_grad=-3.741418 total_sfo_calls=12000

Final metrics:
FINAL_METRICS final_gradient_norm=0.021554 score=-0.021554 auc_log_iteration_log_grad=-0.794382 bilinear_final_gradient

AssistantStep 3edit

Tool Input

1{
2  "start_line": 24,
3  "end_line": 79,
4  "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    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    }\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    tau = float(hyperparameters[\"tau\"])\n    lam = float(hyperparameters[\"lambda\"])\n    gamma = float(hyperparameters[\"gamma\"])\n    z = as_vector(state[\"z\"], expected_dim=2 * problem.dim)\n    step_index = int(state.get(\"step_index\", 0))\n    weight_sum = float(state.get(\"weight_sum\", 0.0))\n    weighted_flow_sum = as_vector(state.get(\"weighted_flow_sum\", np.zeros_like(z)), expected_dim=2 * problem.dim)\n\n    g = oracle.grad(z)\n    anchor_z = tau * lam * (weighted_flow_sum - weight_sum * z)\n    w = z - tau * g + anchor_z + oracle.noise()\n    gw = oracle.grad(w)\n    anchor_w = tau * lam * (weighted_flow_sum - weight_sum * w)\n    z_next = z - tau * gw + anchor_w + oracle.noise()\n\n    current_weight = gamma * (1.0 + gamma) ** (step_index + 1)\n    next_state = {\n        \"z\": z_next,\n        \"step_index\": step_index + 1,\n        \"weight_sum\": weight_sum + current_weight,\n        \"weighted_flow_sum\": weighted_flow_sum + current_weight * z_next,\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    if problem_name == \"bilinear\":\n        return {\"tau\": 0.1, \"lambda\": 0.1, \"gamma\": 0.001}\n    if problem_name == \"delta_nu\":\n        return {\"tau\": 1.0, \"lambda\": 0.01, \"gamma\": 0.0001}\n    raise KeyError(f\"Unknown problem: {problem_name}\")",
5  "filename": "RAIN/optimization_convex_concave/custom_strategy.py",
6  "op": "replace"
7}