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Model: deepseek-reasoner
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Messages: 20
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Task: optimization-bilevel

Optimization Bilevel

Research Question

Can you improve a fixed bilevel-optimization benchmark based on Shen and Chen's penalty-based bilevel gradient descent experiments by selecting a better supported method and tuning only paper-style strategy hyperparameters?

What You Can Modify

Edit only penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py inside the editable block containing:

  1. get_toy_strategy()
  2. get_hyperclean_strategy(net)

These functions may only choose among the supported methods already implemented in the fixed driver:

  • Toy mode: v_pbgd, g_pbgd
  • Data hyper-cleaning mode: v_pbgd, g_pbgd, rhg, t_rhg

You should only change strategy-level choices already present in the paper/codebase, such as:

  • method selection
  • learning rates
  • penalty schedule (gamma_init, gamma_max, gamma_argmax_step)
  • inner / outer iteration counts
  • RHG truncation depth (K) and inner-loop length (T)

Do not rewrite the driver, dataset split, pollution protocol, metrics, or model architectures.

Fixed Setup

Toy / Numerical Verification

  • Problem definition follows Section 5.1 / 6.1 of the paper
  • x is projected to [0, 3]
  • 1000 random initial points are sampled as in the official toy script
  • Primary metric: convergence_steps
  • Secondary metrics: success_rate, final_residual, runtime_sec

Data Hyper-Cleaning

  • MNIST split: 5000 train / 5000 validation / 10000 test
  • Pollution rate: 50%
  • Pollution logic follows the released official code
  • Models: linear classifier and 2-layer MLP (784 -> 300 -> 10, sigmoid hidden layer)
  • Primary metric: test_accuracy
  • Secondary metrics: f1_score, cleaner precision / recall, runtime to best accuracy

Reference Files

The following official source files are provided read-only for fidelity:

  • penalized-bilevel-gradient-descent/V-PBGD/toy/toy.py
  • penalized-bilevel-gradient-descent/V-PBGD/data-hyper-cleaning/data_hyper_clean.py
  • penalized-bilevel-gradient-descent/G-PBGD/data_hyper_clean_gpbgd.py
  • penalized-bilevel-gradient-descent/RHG/data_hyper_clean_rhg.py
  • penalized-bilevel-gradient-descent/RHG/hypergrad/hypergradients.py

Evaluation

The task runs three benchmark commands:

  1. toy-convergence
  2. hyperclean-linear
  3. hyperclean-mlp

Each command prints structured TRAIN_METRICS and FINAL_METRICS lines. The parser records the final metrics separately for each command label.

Hints

  • The paper's official hyperparameters are already a strong starting point for V-PBGD.
  • G-PBGD is competitive but can be sensitive to the penalty schedule.
  • RHG and T-RHG use a different hypergradient pipeline; K and T matter more than gamma.
  • Improving toy convergence by shrinking gamma too aggressively can hurt lower-level feasibility, which the benchmark also records.

penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py [EDITABLE — lines 216–253 only]

     1: """Optim
AssistantStep 1test
AssistantStep 1edit
Tool Input
1{
2  "op": "replace",
3  "filename": "penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py",
4  "start_line": 216,
5  "end_line": 253,
6  "content": "def get_toy_strategy() -> ToyStrategy:\n    return ToyStrategy(\n        method=\"v_pbgd\",\n        gams=(1.0, 10.0),\n        alpha0=0.1,\n    )\n\n\ndef get_hyperclean_strategy(net: str) -> HypercleanStrategy:\n    if net == \"linear\":\n        return HypercleanStrategy(\n            method=\"v_pbgd\",\n            lrx=0.15,\n            lry=0.15,\n            lr_inner=0.01,\n            gamma_init=0.0,\n            gamma_max=0.3,\n            gamma_argmax_step=25_000,\n            outer_itr=40_000,\n            inner_itr=1,\n            reg=0.0,\n            eval_interval=10,\n        )\n    if net == \"mlp\":\n        return HypercleanStrategy(\n            method=\"g_pbgd\",\n            lrx=0.3,\n            lry=0.5,\n            gamma_init=0.0,\n            gamma_max=30.0,\n            gamma_argmax_step=20_000,\n            outer_itr=60_000,\n            reg=0.0,\n            eval_interval=10,\n        )\n    raise ValueError(f\"Unsupported network: {net}\")"
7}
Tool ResultStep 1
OK: Replaced lines 216..253 with 36 line(s) in penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py. Editable range: 216–251.

[Current file: penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py | editable: 216–251 | total: 930 lines]
   213| # =====================================================================
   214| # EDITABLE: select supported methods and paper-style hyperparameters only
   215| # =====================================================================
   216  def get_toy_strategy() -> ToyStrategy:
   217      return ToyStrategy(
   218          method="v_pbgd",
   219          gams=(1.0, 10.0),
   220          alpha0=0.1,
   221      )
   222  
   223  
   224  def get_hyperclean_strategy(net: str) -> HypercleanStrategy:
   225      if net == "linear":
   226          return HypercleanStrategy(
   227              method="v_pbgd",
   228              lrx=0.15,
   229              lry=0.15,
   230              lr_inner=0.01,
   231              g
AssistantStep 2test
Tool ResultStep 2
[Test #1] (2 tests remaining; call submit(n=1) to submit this result)

### toy-convergence (scripts/toy_convergence.sh)
Training progress:
TRAIN_METRICS run=995 step=94 objective=-0.284359 residual=0.529694 projected_grad=0.000010 success=1
TRAIN_METRICS run=996 step=105 objective=-0.284358 residual=0.529695 projected_grad=0.000010 success=1
TRAIN_METRICS run=997 step=53 objective=-0.169882 residual=0.315812 projected_grad=0.000009 success=1
TRAIN_METRICS run=998 step=103 objective=-0.284359 residual=0.529694 projected_grad=0.000009 success=1
TRAIN_METRICS run=999 step=35 objective=-0.169886 residual=0.315815 projected_grad=0.000008 success=1

Final metrics:
FINAL_METRICS convergence_steps=7711.351000 median_steps=101.000000 final_residual=0.474206 final_projected_grad=1.256463 success_rate=0.809000 runtime_sec=7.225114 score=7711.351000

### hyperclean-linear (scripts/hyperclean_linear.sh)
[COMMAND FAILED exit=1]
Traceback (most recent call last):
  File "/srv/home/bohanlyu/MLS-Bench/
AssistantStep 3edit
Tool Input
1{
2  "op": "replace",
3  "filename": "penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py",
4  "start_line": 216,
5  "end_line": 251,
6  "content": "def get_toy_strategy() -> ToyStrategy:\n    return ToyStrategy(\n        method=\"v_pbgd\",\n        gams=(5.0,),\n        alpha0=0.1,\n    )\n\n\ndef get_hyperclean_strategy(net: str) -> HypercleanStrategy:\n    if net == \"linear\":\n        return HypercleanStrategy(\n            method=\"v_pbgd\",\n            lrx=0.1,\n            lry=0.1,\n            lr_inner=0.01,\n            gamma_init=0.0,\n            gamma_max=0.2,\n            gamma_argmax_step=30_000,\n            outer_itr=40_000,\n            inner_itr=1,\n            reg=0.0,\n            eval_interval=10,\n        )\n    if net == \"mlp\":\n        return HypercleanStrategy(\n            method=\"v_pbgd\",\n            lrx=0.1,\n            lry=0.01,\n            lr_inner=0.01,\n            gamma_init=0.0,\n            gamma_max=0.1,\n            gamma_argmax_step=10_000,\n            outer_itr=80_000,\n            inner_itr=1,\n            reg=0.0,\n            eval_interval=10,\n        )\n    raise ValueError(f\"Unsupported network: {net}\")"
7}
Tool ResultStep 3
OK: Replaced lines 216..251 with 38 line(s) in penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py. Editable range: 216–253.

[Current file: penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py | editable: 216–253 | total: 932 lines]
   213| # =====================================================================
   214| # EDITABLE: select supported methods and paper-style hyperparameters only
   215| # =====================================================================
   216  def get_toy_strategy() -> ToyStrategy:
   217      return ToyStrategy(
   218          method="v_pbgd",
   219          gams=(5.0,),
   220          alpha0=0.1,
   221      )
   222  
   223  
   224  def get_hyperclean_strategy(net: str) -> HypercleanStrategy:
   225      if net == "linear":
   226          return HypercleanStrategy(
   227              method="v_pbgd",
   228              lrx=0.1,
   229              lry=0.1,
   230              lr_inner=0.01,
   231              gamma_in
AssistantStep 4test
Tool ResultStep 4
[Test #2] (1 test remaining; call submit(n=2) to submit this result)

### toy-convergence (scripts/toy_convergence.sh)
Training progress:
TRAIN_METRICS run=995 step=145 objective=0.367849 residual=0.087143 projected_grad=0.000010 success=1
TRAIN_METRICS run=996 step=150 objective=0.367849 residual=0.087143 projected_grad=0.000010 success=1
TRAIN_METRICS run=997 step=115 objective=0.147460 residual=0.049164 projected_grad=0.000010 success=1
TRAIN_METRICS run=998 step=148 objective=0.367849 residual=0.087143 projected_grad=0.000009 success=1
TRAIN_METRICS run=999 step=109 objective=0.147459 residual=0.049165 projected_grad=0.000010 success=1

Final metrics:
FINAL_METRICS convergence_steps=129.169000 median_steps=143.000000 final_residual=0.067240 final_projected_grad=0.000009 success_rate=1.000000 runtime_sec=0.335501 score=129.169000

### hyperclean-linear (scripts/hyperclean_linear.sh)
[COMMAND FAILED exit=1]
Traceback (most recent call last):
  File "/srv/home/bohanlyu/MLS-Bench/vendo
AssistantStep 1test
Tool ResultStep 1
[Test #1] (2 tests remaining; call submit(n=1) to submit this result)

### toy-convergence (scripts/toy_convergence.sh)
Training progress:
TRAIN_METRICS run=995 step=307 objective=0.423728 residual=0.038709 projected_grad=0.000010 success=1
TRAIN_METRICS run=996 step=312 objective=0.423728 residual=0.038709 projected_grad=0.000010 success=1
TRAIN_METRICS run=997 step=204 objective=0.174725 residual=0.023824 projected_grad=0.000010 success=1
TRAIN_METRICS run=998 step=309 objective=0.423728 residual=0.038709 projected_grad=0.000010 success=1
TRAIN_METRICS run=999 step=198 objective=0.174724 residual=0.023825 projected_grad=0.000010 success=1

Final metrics:
FINAL_METRICS convergence_steps=261.256000 median_steps=303.000000 final_residual=0.030345 final_projected_grad=0.000010 success_rate=1.000000 runtime_sec=0.512825 score=261.256000

### hyperclean-linear (scripts/hyperclean_linear.sh)
Training progress:
TRAIN_METRICS step=39950 train_loss=1.418569 val_loss=0.172322 test_accuracy=88.1
AssistantStep 2edit
Tool Input
1{
2  "op": "replace",
3  "filename": "penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py",
4  "start_line": 216,
5  "end_line": 253,
6  "content": "def get_toy_strategy() -> ToyStrategy:\n    return ToyStrategy(\n        method=\"v_pbgd\",\n        gams=(1.0, 10.0, 100.0),\n        alpha0=0.1,\n    )\n\n\ndef get_hyperclean_strategy(net: str) -> HypercleanStrategy:\n    if net == \"linear\":\n        return HypercleanStrategy(\n            method=\"v_pbgd\",\n            lrx=0.1,\n            lry=0.1,\n            lr_inner=0.01,\n            gamma_init=0.0,\n            gamma_max=1.0,\n            gamma_argmax_step=30_000,\n            outer_itr=40_000,\n            inner_itr=1,\n            reg=0.0,\n            eval_interval=10,\n        )\n    if net == \"mlp\":\n        return HypercleanStrategy(\n            method=\"g_pbgd\",\n            lrx=0.5,\n            lry=0.5,\n            gamma_init=0.0,\n            gamma_max=37.0,\n            gamma_argmax_step=30_000,\n            outer_itr=50_000,\n            reg=0.0,\n            eval_interval=10,\n        )\n    raise ValueError(f\"Unsupported network: {net}\")"
7}
Tool ResultStep 2
OK: Replaced lines 216..253 with 36 line(s) in penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py. Editable range: 216–251.

[Current file: penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py | editable: 216–251 | total: 930 lines]
   213| # =====================================================================
   214| # EDITABLE: select supported methods and paper-style hyperparameters only
   215| # =====================================================================
   216  def get_toy_strategy() -> ToyStrategy:
   217      return ToyStrategy(
   218          method="v_pbgd",
   219          gams=(1.0, 10.0, 100.0),
   220          alpha0=0.1,
   221      )
   222  
   223  
   224  def get_hyperclean_strategy(net: str) -> HypercleanStrategy:
   225      if net == "linear":
   226          return HypercleanStrategy(
   227              method="v_pbgd",
   228              lrx=0.1,
   229              lry=0.1,
   230              lr_inner=0.01,
   231
AssistantStep 3test
Tool ResultStep 3
[Test #2] (1 test remaining; call submit(n=2) to submit this result)

### toy-convergence (scripts/toy_convergence.sh)
[output file not found: /srv/home/bohanlyu/MLS-Bench/logs/optimization-bilevel/deepseek-reasoner_20260405_233840/20260405_235315/group_1/toy-convergence_s42.out]

### hyperclean-linear (scripts/hyperclean_linear.sh)
Training progress:
TRAIN_METRICS step=39950 train_loss=0.888114 val_loss=0.352052 test_accuracy=86.020 f1_score=89.197 cleaner_precision=0.850254 cleaner_recall=0.938000 penalty_gap=0.104708 iter_time=0.001976
TRAIN_METRICS step=39960 train_loss=0.888077 val_loss=0.352039 test_accuracy=86.020 f1_score=89.197 cleaner_precision=0.850254 cleaner_recall=0.938000 penalty_gap=0.104698 iter_time=0.002033
TRAIN_METRICS step=39970 train_loss=0.888041 val_loss=0.352026 test_accuracy=86.020 f1_score=89.197 cleaner_precision=0.850254 cleaner_recall=0.938000 penalty_gap=0.104687 iter_time=0.001888
TRAIN_METRICS step=39980 train_loss=0.888004 val_loss=0.352013 test_accur
AssistantStep 4edit
Tool Input
1{
2  "op": "replace",
3  "filename": "penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py",
4  "start_line": 216,
5  "end_line": 251,
6  "content": "def get_toy_strategy() -> ToyStrategy:\n    return ToyStrategy(\n        method=\"v_pbgd\",\n        gams=(5.0,),\n        alpha0=0.2,\n    )\n\n\ndef get_hyperclean_strategy(net: str) -> HypercleanStrategy:\n    if net == \"linear\":\n        return HypercleanStrategy(\n            method=\"v_pbgd\",\n            lrx=0.2,\n            lry=0.2,\n            lr_inner=0.01,\n            gamma_init=0.1,\n            gamma_max=2.0,\n            gamma_argmax_step=5_000,\n            outer_itr=40_000,\n            inner_itr=1,\n            reg=0.0,\n            eval_interval=10,\n        )\n    if net == \"mlp\":\n        return HypercleanStrategy(\n            method=\"g_pbgd\",\n            lrx=0.5,\n            lry=0.5,\n            gamma_init=0.0,\n            gamma_max=37.0,\n            gamma_argmax_step=10_000,\n            outer_itr=50_000,\n            reg=0.0,\n            eval_interval=10,\n        )\n    raise ValueError(f\"Unsupported network: {net}\")"
7}
Tool ResultStep 4
OK: Replaced lines 216..251 with 36 line(s) in penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py. Editable range: 216–251.

[Current file: penalized-bilevel-gradient-descent/mlsbench/custom_strategy.py | editable: 216–251 | total: 930 lines]
   213| # =====================================================================
   214| # EDITABLE: select supported methods and paper-style hyperparameters only
   215| # =====================================================================
   216  def get_toy_strategy() -> ToyStrategy:
   217      return ToyStrategy(
   218          method="v_pbgd",
   219          gams=(5.0,),
   220          alpha0=0.2,
   221      )
   222  
   223  
   224  def get_hyperclean_strategy(net: str) -> HypercleanStrategy:
   225      if net == "linear":
   226          return HypercleanStrategy(
   227              method="v_pbgd",
   228              lrx=0.2,
   229              lry=0.2,
   230              lr_inner=0.01,
   231              gamma_in
AssistantStep 5test
Tool ResultStep 5
[Test #3] (0 tests remaining)

### toy-convergence (scripts/toy_convergence.sh)
Training progress:
TRAIN_METRICS run=995 step=69 objective=0.367849 residual=0.087143 projected_grad=0.000010 success=1
TRAIN_METRICS run=996 step=72 objective=0.367849 residual=0.087143 projected_grad=0.000008 success=1
TRAIN_METRICS run=997 step=20000 objective=0.299583 residual=0.169489 projected_grad=4.059039 success=0
TRAIN_METRICS run=998 step=70 objective=0.367849 residual=0.087143 projected_grad=0.000010 success=1
TRAIN_METRICS run=999 step=20000 objective=0.042563 residual=0.056599 projected_grad=4.059039 success=0

Final metrics:
FINAL_METRICS convergence_steps=7363.511000 median_steps=72.000000 final_residual=0.150988 final_projected_grad=3.812279 success_rate=0.634000 runtime_sec=14.206083 score=7363.511000

### hyperclean-linear (scripts/hyperclean_linear.sh)
Training progress:
TRAIN_METRICS step=39950 train_loss=0.740563 val_loss=0.470222 test_accuracy=82.400 f1_score=82.400 cleaner_precision=