Agent Conversation: openai/gpt-5.4-pro

Model: openai/gpt-5.4-pro

Total steps: 6

Messages: 13

UserStep 0

Task: optimization-dp-sgd

Differentially Private SGD: Privacy-Utility Optimization

Research Question

Design an improved DP-SGD variant that achieves better privacy-utility tradeoff — higher test accuracy under the same (epsilon, delta)-differential privacy budget.

Background

Differentially Private Stochastic Gradient Descent (DP-SGD) [Abadi et al., 2016] enables training deep learning models with formal privacy guarantees. The core mechanism has two steps: (1) clip each per-sample gradient to a fixed norm C, and (2) add calibrated Gaussian noise proportional to C. The noise level is determined by the desired privacy budget (epsilon, delta).

The standard approach uses a fixed clipping threshold and constant noise throughout training, which is suboptimal: gradient magnitudes change during training, the fixed threshold either over-clips (losing signal) or under-clips (adding excess noise), and the uniform noise allocation ignores the varying informativeness of gradients across training stages.

Task

Modify the DPMechanism class in custom_dpsgd.py. Your mechanism receives per-sample gradients and must return aggregated noised gradients. You control the gradient clipping strategy, noise calibration, and any per-step adaptations.

Interface

class DPMechanism:
    def __init__(self, max_grad_norm, noise_multiplier, n_params,
                 dataset_size, batch_size, epochs, target_epsilon, target_delta):
        ...

    def clip_and_noise(self, per_sample_grads, step, epoch) -> list[Tensor]:
        # per_sample_grads: list of tensors [B, *param_shape]
        # Returns: list of noised gradients [*param_shape]
        ...

    def get_effective_sigma(self, step, epoch) -> float:
        # Returns current noise multiplier for privacy accounting
        ...

Constraints

The total privacy budget (target_epsilon, target_delta) is FIXED and checked externally.
The model architecture, data pipeline, optimizer, and training loop are FIXED.
Focus on algorithmic innovation in the DP mechanism: clipping strategies, noise schedules, gradient processing.
Available imports: torch, math, numpy (via the FIXED section), scipy.optimize.

Evaluation

Trained and evaluated on three datasets at epsilon=3.0, delta=1e-5:

MNIST (28x28 grayscale digits, 10 classes)
Fashion-MNIST (28x28 grayscale clothing, 10 classes)
CIFAR-10 (32x32 color images, 10 classes)

Metric: test accuracy (higher is better) under the same privacy budget.

Hints

Adaptive clipping: adjust the clipping threshold based on observed gradient norms (e.g., track quantiles).
Noise scheduling: allocate more noise to early training (large gradients) and less to later training (refined gradients).
Gradient normalization: normalize per-sample gradients instead of clipping to a fixed threshold.
Per-layer strategies: clip/noise at the layer level rather than globally.
Momentum-based variance reduction: use gradient moment

AssistantStep 1edit

Tool Input

1{
2  "op": "replace",
3  "filename": "opacus/custom_dpsgd.py",
4  "content": "class DPMechanism:\n    \"\"\"Selective layerwise clipping with cosine privacy-budget reallocation.\n\n    Two changes over standard DP-SGD:\n    1) Per-sample *water-filling* clipping across parameter tensors: for each\n       sample, only layers with unusually large norms are clipped, while small\n       layers are kept intact. This preserves weak but useful gradients that\n       global clipping would unnecessarily shrink.\n    2) A data-independent cosine noise schedule with exact harmonic-mean\n       accounting, so later optimization steps receive slightly less noise\n       without exceeding the same total privacy budget.\n    \"\"\"\n\n    def __init__(self, max_grad_norm, noise_multiplier, n_params,\n                 dataset_size, batch_size, epochs, target_epsilon, target_delta):\n        self.max_grad_norm = max_grad_norm\n        self.noise_multiplier = noise_multiplier\n        self.n_params = n_params\n        self.dataset_size = dataset_size\n        self.batch_size = batch_size\n        self.epochs = epochs\n        self.target_epsilon = target_epsilon\n        self.target_delta = target_delta\n\n        self.total_steps = max(1, (dataset_size // batch_size) * epochs)\n        self._bisection_steps = 14\n\n        # Smoothly shift privacy budget toward later, more refined updates.\n        amp = 0.25\n        idx = np.arange(self.total_steps, dtype=np.float64)\n        progress = (idx + 0.5) / self.total_steps\n        rel_sigma = 1.0 + amp * np.cos(np.pi * progress)  # early > 1, late < 1\n        scale = math.sqrt(np.mean(1.0 / (rel_sigma ** 2)))\n        self.sigma_schedule = [float(noise_multiplier * scale * r) for r in rel_sigma]\n\n        self.prefix_inv_sq = [0.0]\n        acc = 0.0\n        for sigma in self.sigma_schedule:\n            acc += 1.0 / (sigma * sigma)\n            self.prefix_inv_sq.append(acc)\n\n    def _waterfill_scales(self, layer_norms):\n        \"\"\"Return per-sample, per-layer scales with total norm <= max_grad_norm.\n\n        For each sample i, choose a cap tau_i so clipped layer norms become\n        min(||g_ij||, tau_i) and the concatenated clipped gradient has norm C.\n        This clips only the dominant layers instead of shrinking all layers.\n        \"\"\"\n        scales = torch.ones_like(layer_norms)\n        target_sq = self.max_grad_norm * self.max_grad_norm\n        total_sq = (layer_norms * layer_norms).sum(dim=1)\n        active = total_sq > target_sq\n        if not active.any():\n            return scales\n\n        ln = layer_norms[active]\n        low = torch.zeros(ln.size(0), device=ln.device, dtype=ln.dtype)\n        high = ln.max(dim=1).values\n        for _ in range(self._bisection_steps):\n            mid = 0.5 * (low + high)\n            capped_sq = torch.minimum(ln, mid.unsqueeze(1)).pow(2).sum(dim=1)\n            too_big = capped_sq > target_sq\n            high = torch.where(too_big, mid, high)\n            low = torch.where(too_big, low, mid)\n\n        tau = 0.5 * (low + high)\n        scales[active] = torch.minimum(\n            torch.ones_like(ln), tau.unsqueeze(1) / ln.clamp(min=1e-12)\n        )\n        return scales\n\n    def clip_and_noise(self, per_sample_grads, step, epoch):\n        batch_size = per_sample_grads[0].shape[0]\n        layer_norms = torch.stack(\n            [g.reshape(batch_size, -1).norm(2, dim=1) for g in per_sample_grads], dim=1\n        )\n        scales = self._waterfill_scales(layer_norms)\n\n        sigma = self.sigma_schedule[min(step, self.total_steps - 1)]\n        noise_std = sigma * self.max_grad_norm / batch_size\n\n        noised_grads = []\n        for j, g in enumerate(per_sample_grads):\n            shape = [batch_size] + [1] * (g.dim() - 1)\n            clipped = g * scales[:, j].reshape(shape)\n            avg = clipped.mean(dim=0)\n            noised_grads.append(avg + torch.randn_like(avg) * noise_std)\n        return noised_grads\n\n    def get_effective_sigma(self, step, epoch):\n        if step <= 0:\n            return self.sigma_schedule[0]\n        step = min(step, self.total_steps)\n        return math.sqrt(step / self.prefix_inv_sq[step])",
5  "after_line": 171,
6  "start_line": 172,
7  "end_line": 229
8}

Tool ResultStep 1

OK: Replaced lines 172..229 with 94 line(s) in opacus/custom_dpsgd.py. Editable range: 152–269.

[Current file: opacus/custom_dpsgd.py | editable: 152–269 | total: 581 lines]
   149|     return (sigma_low + sigma_high) / 2
   150| 
   151| 
   152  # =====================================================================
   153  # EDITABLE SECTION START (lines 152-233)
   154  # =====================================================================
   155  # DPMechanism: Controls how per-sample gradients are clipped and noised.
   156  #
   157  # Interface contract:
   158  #   __init__(self, max_grad_norm, noise_multiplier, n_params, dataset_size,
   159  #            batch_size, epochs, target_epsilon, target_delta)
   160  #   clip_and_noise(self, per_sample_grads, step, epoch) -> noised_gradient
   161  #   get_effective_sigma(self, step, epoch) -> float
   162  #
   163  # The mechanism receives per-sample gradients (list of tensors, each [B, *param_shape])
   164  # and must return

AssistantStep 2test

Tool ResultStep 2

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


## Seed 42

### mnist (scripts/mnist.sh)
[output file not found: /srv/home/bohanlyu/MLS-Bench/logs/optimization-dp-sgd/openai_gpt-5.4-pro_20260405_233917/20260406_000504/group_1_0/mnist_s42.out]

### fmnist (scripts/fmnist.sh)
Training progress (fmnist):
TRAIN_METRICS epoch=4 step=902 loss=0.972050 accuracy=79.12
TRAIN_METRICS epoch=5 step=986 loss=0.962547 accuracy=78.87
TRAIN_METRICS epoch=5 step=1036 loss=0.951078 accuracy=79.22
TRAIN_METRICS epoch=5 step=1086 loss=0.940222 accuracy=79.59
TRAIN_METRICS epoch=5 step=1136 loss=0.943287 accuracy=79.69
Epoch summaries (fmnist):
Epoch 3/5: train_loss=0.9978 train_acc=78.12% test_loss=1.0113 test_acc=77.61% epsilon_spent=1.95 sigma=0.2782
Epoch 4/5: train_loss=0.9653 train_acc=79.19% test_loss=0.9650 test_acc=78.75% epsilon_spent=2.47 sigma=0.2567
Epoch 5/5: train_loss=0.9448 train_acc=79.66% test_loss=0.9987 test_acc=78.67% epsilon_spent=3.00 sigma=0.2385
accuracy_fm

AssistantStep 3edit

Tool Input

1{
2  "op": "replace",
3  "filename": "opacus/custom_dpsgd.py",
4  "content": "class DPMechanism:\n    \"\"\"Progressive radial clipping with exact privacy-budget reallocation.\n\n    We interpolate between two bounded transforms of each per-sample gradient:\n    - standard DP clipping, which preserves magnitude for small gradients;\n    - AUTO-S-style radial normalization, which boosts weak late-stage gradients.\n\n    The AUTO-S component is gradually increased during training, while the\n    Gaussian noise follows a mild cosine schedule with exact harmonic-mean\n    accounting so the overall privacy budget remains unchanged.\n    \"\"\"\n\n    def __init__(self, max_grad_norm, noise_multiplier, n_params,\n                 dataset_size, batch_size, epochs, target_epsilon, target_delta):\n        self.max_grad_norm = max_grad_norm\n        self.noise_multiplier = noise_multiplier\n        self.n_params = n_params\n        self.dataset_size = dataset_size\n        self.batch_size = batch_size\n        self.epochs = epochs\n        self.target_epsilon = target_epsilon\n        self.target_delta = target_delta\n\n        self.total_steps = max(1, (dataset_size // batch_size) * epochs)\n        self.gamma = 0.02\n        self.mix_start = 0.15\n        self.mix_end = 0.80\n\n        # Gentle schedules for short runs, stronger reallocation for long runs.\n        amp = 0.10 + 0.15 * min(1.0, epochs / 30.0)\n        idx = np.arange(self.total_steps, dtype=np.float64)\n        progress = (idx + 0.5) / self.total_steps\n        rel_sigma = 1.0 + amp * np.cos(np.pi * progress)  # early > 1, late < 1\n        scale = math.sqrt(np.mean(1.0 / (rel_sigma ** 2)))\n        self.sigma_schedule = [float(noise_multiplier * scale * r) for r in rel_sigma]\n\n        self.prefix_inv_sq = [0.0]\n        acc = 0.0\n        for sigma in self.sigma_schedule:\n            acc += 1.0 / (sigma * sigma)\n            self.prefix_inv_sq.append(acc)\n\n    def _mix_weight(self, step):\n        if self.total_steps <= 1:\n            return self.mix_end\n        progress = min(1.0, max(0.0, step / (self.total_steps - 1)))\n        smooth = 0.5 - 0.5 * math.cos(math.pi * progress)\n        return self.mix_start + (self.mix_end - self.mix_start) * smooth\n\n    def clip_and_noise(self, per_sample_grads, step, epoch):\n        batch_size = per_sample_grads[0].shape[0]\n        flat = torch.cat([g.reshape(batch_size, -1) for g in per_sample_grads], dim=1)\n        norms = flat.norm(2, dim=1).clamp(min=1e-12)\n\n        c = self.max_grad_norm\n        std_scale = (c / norms).clamp(max=1.0)\n        auto_scale = c / (norms + self.gamma * c)\n        mix = self._mix_weight(step)\n        scale = (1.0 - mix) * std_scale + mix * auto_scale\n\n        sigma = self.sigma_schedule[min(step, self.total_steps - 1)]\n        noise_std = sigma * c / batch_size\n\n        noised_grads = []\n        for g in per_sample_grads:\n            shape = [batch_size] + [1] * (g.dim() - 1)\n            transformed = g * scale.reshape(shape)\n            avg = transformed.mean(dim=0)\n            noised_grads.append(avg + torch.randn_like(avg) * noise_std)\n        return noised_grads\n\n    def get_effective_sigma(self, step, epoch):\n        if step <= 0:\n            return self.sigma_schedule[0]\n        step = min(step, self.total_steps)\n        return math.sqrt(step / self.prefix_inv_sq[step])",
5  "after_line": 171,
6  "start_line": 172,
7  "end_line": 265
8}

Tool ResultStep 3

OK: Replaced lines 172..265 with 76 line(s) in opacus/custom_dpsgd.py. Editable range: 152–251.

[Current file: opacus/custom_dpsgd.py | editable: 152–251 | total: 563 lines]
   149|     return (sigma_low + sigma_high) / 2
   150| 
   151| 
   152  # =====================================================================
   153  # EDITABLE SECTION START (lines 152-233)
   154  # =====================================================================
   155  # DPMechanism: Controls how per-sample gradients are clipped and noised.
   156  #
   157  # Interface contract:
   158  #   __init__(self, max_grad_norm, noise_multiplier, n_params, dataset_size,
   159  #            batch_size, epochs, target_epsilon, target_delta)
   160  #   clip_and_noise(self, per_sample_grads, step, epoch) -> noised_gradient
   161  #   get_effective_sigma(self, step, epoch) -> float
   162  #
   163  # The mechanism receives per-sample gradients (list of tensors, each [B, *param_shape])
   164  # and must return

AssistantStep 4test

Tool ResultStep 4

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

### mnist (scripts/mnist.sh)
Calibrated noise_multiplier sigma=0.2385 for epsilon=3.0, delta=1e-05, steps=1170, q=0.0043
Model: MNISTNet, Parameters: 26010


### fmnist (scripts/fmnist.sh)
Training progress (fmnist):
TRAIN_METRICS epoch=1 step=50 loss=1.493073 accuracy=46.79

### cifar10 (scripts/cifar10.sh)
Training progress (cifar10):
TRAIN_METRICS epoch=29 step=5560 loss=1.514568 accuracy=55.23
TRAIN_METRICS epoch=29 step=5610 loss=1.514746 accuracy=55.24
TRAIN_METRICS epoch=30 step=5705 loss=1.516016 accuracy=55.60
TRAIN_METRICS epoch=30 step=5755 loss=1.522833 accuracy=55.19
TRAIN_METRICS epoch=30 step=5805 loss=1.522484 accuracy=55.21
Epoch summaries (cifar10):
Epoch 28/30: train_loss=1.5188 train_acc=55.20% test_loss=1.5479 test_acc=54.55% epsilon_spent=2.82 sigma=0.6548
Epoch 29/30: train_loss=1.5195 train_acc=55.22% test_loss=1.5527 test_acc=54.48% epsilon_spent=2.91 sigma=0.6474
Epoch 30/30: train_loss=1.51

AssistantStep 5edit

Tool Input

1{
2  "op": "replace",
3  "filename": "opacus/custom_dpsgd.py",
4  "content": "        self.total_steps = max(1, (dataset_size // batch_size) * epochs)\n        run_frac = min(1.0, epochs / 30.0)\n        self.gamma = 0.03 - 0.01 * run_frac\n        self.mix_start = 0.05 + 0.10 * run_frac\n        self.mix_end = 0.55 + 0.25 * run_frac",
5  "after_line": 194,
6  "start_line": 195,
7  "end_line": 198
8}

Tool ResultStep 5

OK: Replaced lines 195..198 with 5 line(s) in opacus/custom_dpsgd.py. Editable range: 152–252.

[Current file: opacus/custom_dpsgd.py | editable: 152–252 | total: 564 lines]
   149|     return (sigma_low + sigma_high) / 2
   150| 
   151| 
   152  # =====================================================================
   153  # EDITABLE SECTION START (lines 152-233)
   154  # =====================================================================
   155  # DPMechanism: Controls how per-sample gradients are clipped and noised.
   156  #
   157  # Interface contract:
   158  #   __init__(self, max_grad_norm, noise_multiplier, n_params, dataset_size,
   159  #            batch_size, epochs, target_epsilon, target_delta)
   160  #   clip_and_noise(self, per_sample_grads, step, epoch) -> noised_gradient
   161  #   get_effective_sigma(self, step, epoch) -> float
   162  #
   163  # The mechanism receives per-sample gradients (list of tensors, each [B, *param_shape])
   164  # and must return

AssistantStep 6test

Tool ResultStep 6

[Test #3] (0 tests remaining)


## Seed 42

### mnist (scripts/mnist.sh)
Training progress (mnist):
TRAIN_METRICS epoch=4 step=902 loss=0.247150 accuracy=95.79
TRAIN_METRICS epoch=5 step=986 loss=0.258026 accuracy=95.69
TRAIN_METRICS epoch=5 step=1036 loss=0.246426 accuracy=95.76
TRAIN_METRICS epoch=5 step=1086 loss=0.250779 accuracy=95.78
TRAIN_METRICS epoch=5 step=1136 loss=0.252588 accuracy=95.80
Epoch summaries (mnist):
Epoch 3/5: train_loss=0.2726 train_acc=95.20% test_loss=0.2404 test_acc=95.79% epsilon_spent=2.13 sigma=0.2556
Epoch 4/5: train_loss=0.2573 train_acc=95.71% test_loss=0.2282 test_acc=96.08% epsilon_spent=2.58 sigma=0.2464
Epoch 5/5: train_loss=0.2512 train_acc=95.86% test_loss=0.2257 test_acc=96.15% epsilon_spent=3.00 sigma=0.2385
accuracy_mnist: 96.1500
epsilon_mnist: 3.0016
best_accuracy_mnist: 96.1500

### fmnist (scripts/fmnist.sh)
Training progress (fmnist):
TRAIN_METRICS epoch=4 step=902 loss=1.001485 accuracy=80.70
TRAIN_METRICS epoch=5 step=986 loss=1.008733