Agent Conversation: anthropic/claude-opus-4.6
Model: anthropic/claude-opus-4.6
Total steps: 7
Messages: 15
UserStep 0
Task: optimization-variance-reduction
Variance Reduction for Stochastic Optimization
Research Question
Design an improved variance reduction strategy for stochastic gradient descent on finite-sum optimization problems. Your method should accelerate convergence compared to vanilla mini-batch SGD by reducing the variance of gradient estimates.
Background
Many machine learning problems take the form of finite-sum optimization:
min_x F(x) = (1/n) * sum_{i=1}^{n} f_i(x)
Standard SGD uses a stochastic gradient from a random mini-batch, which has variance proportional to 1/b (where b is the batch size). Variance reduction methods use auxiliary information (snapshots, recursive corrections, momentum) to reduce this variance, enabling faster convergence -- often achieving linear convergence rates for strongly convex problems where SGD only achieves sublinear rates.
Key methods in this area include SVRG (periodic full gradient + control variate), SARAH (recursive gradient correction), STORM (momentum-based online variance reduction), SPIDER, and PAGE.
Task
Modify the VarianceReductionOptimizer class in custom_vr.py (lines 286-370). You must implement:
__init__(self, model, lr, l2_reg, loss_type, n_train, batch_size, device): Initialize any state needed for variance reduction (snapshot parameters, running gradient estimates, buffers, etc.)train_one_epoch(self, X_train, y_train): Train for one epoch over the data, returning a dict with at least'avg_loss'(and optionally'full_grad_count'if you use full gradient computations)
The default implementation is vanilla mini-batch SGD. Your goal is to design a variance reduction mechanism that improves convergence.
Interface
Available helper functions (FIXED, use these for gradient computation):
compute_full_gradient(model, X_train, y_train, loss_type, l2_reg, device)
# -> returns list of gradient tensors (one per parameter)
compute_stochastic_gradient(model, X_batch, y_batch, loss_type, l2_reg)
# -> returns list of gradient tensors for a mini-batch
compute_loss_on_batch(model, X_batch, y_batch, loss_type, l2_reg)
# -> returns scalar loss tensorConstraints
- You may call
compute_full_gradientat most once per epoch - Parameter updates must use
p.data.add_(...)or similar in-place operations - Must work across all three problems with the same code
- The learning rate (
self.lr) and L2 regularization (self.l2_reg) are fixed - Do not modify the model architecture, loss function, or evaluation code
Evaluation
- Problems:
logistic: L2-regularized multinomial logistic regression on MNIST (convex, n=60K, 20 epochs)mlp: 2-layer MLP on CIFAR-10 (non-convex, n=50K, 40 epochs)conditioned: L2-regularized linear regression on synthetic ill-conditioned data (strongly convex, kappa=100, n=10K, 30 epochs)
- Metrics:
best_test_accuracy(logistic, mlp; higher is better) andbest_test_mse(conditioned; lowe
AssistantStep 1edit
Tool Input
1{
2 "error": "Failed to parse tool arguments: Expecting ',' delimiter: line 1 column 94 (char 93)"
3}Tool ResultStep 1
ERROR: Failed to parse tool arguments: Expecting ',' delimiter: line 1 column 94 (char 93)
AssistantStep 2edit
Tool Input
1{
2 "op": "replace",
3 "filename": "opt-vr-bench/custom_vr.py",
4 "start_line": 286,
5 "end_line": 370,
6 "content": "class VarianceReductionOptimizer:\n \"\"\"Momentum-Accelerated SVRG (MA-SVRG).\n\n Combines SVRG control-variate variance reduction with heavy-ball momentum\n for accelerated convergence. SVRG cancels stochastic noise via\n v = g(x)-g(snap)+mu; momentum smooths estimates and provides Polyak-style\n acceleration on ill-conditioned landscapes. Step is scaled so effective\n steady-state learning rate equals base_lr.\n \"\"\"\n\n def __init__(self, model: nn.Module, lr: float, l2_reg: float,\n loss_type: str, n_train: int, batch_size: int,\n device: torch.device):\n self.model = model\n self.lr = lr\n self.l2_reg = l2_reg\n self.loss_type = loss_type\n self.n_train = n_train\n self.batch_size = batch_size\n self.device = device\n self.params = list(model.parameters())\n self.snap = self.mu = self.mbuf = self.eta_max = None\n self.beta = 0.8\n\n def train_one_epoch(self, X_train: torch.Tensor,\n y_train: torch.Tensor) -> dict:\n self.model.train()\n n = X_train.size(0)\n # Snapshot & full gradient (once per epoch)\n self.snap = [p.data.clone() for p in self.params]\n self.mu = compute_full_gradient(\n self.model, X_train, y_train,\n self.loss_type, self.l2_reg, self.device)\n # Init momentum buffer at steady-state value (avoids warm-up lag)\n if self.mbuf is None:\n self.mbuf = [g.clone().div_(1.0 - self.beta) for g in self.mu]\n # Adaptive step sizing (critical for ill-conditioned MSE)\n gnorm = math.sqrt(sum(g.pow(2).sum().item() for g in self.mu))\n pnorm = math.sqrt(sum(\n p.data.pow(2).sum().item() for p in self.params)) + 1e-8\n astep = 0.01 * pnorm / (gnorm + 1e-8)\n if self.loss_type == 'mse':\n if self.eta_max is None: self.eta_max = astep\n else: self.eta_max = min(2.0 * self.eta_max, astep)\n base_lr = min(self.lr, astep, self.eta_max)\n else:\n base_lr = self.lr\n eta = base_lr * (1.0 - self.beta)\n clip_val = max(gnorm * 5.0, 1e-6)\n # Inner SVRG loop with momentum\n indices = torch.randperm(n)\n total_loss, nb = 0.0, 0\n for st in range(0, n, self.batch_size):\n end = min(st + self.batch_size, n)\n Xb = X_train[indices[st:end]].to(self.device)\n yb = y_train[indices[st:end]].to(self.device)\n # Gradient at current params\n self.model.zero_grad()\n loss = compute_loss_on_batch(\n self.model, Xb, yb, self.loss_type, self.l2_reg)\n loss.backward()\n gc = [p.grad.clone() for p in self.params]\n self.model.zero_grad()\n total_loss += loss.item()\n # Gradient at snapshot (same batch for correlated noise cancel)\n saved = [p.data.clone() for p in self.params]\n for p, sp in zip(self.params, self.snap): p.data.copy_(sp)\n gs = compute_stochastic_gradient(\n self.model, Xb, yb, self.loss_type, self.l2_reg)\n for p, s in zip(self.params, saved): p.data.copy_(s)\n # SVRG estimate + gradient clipping + momentum update\n with torch.no_grad():\n vl = [gc[i] - gs[i] + self.mu[i]\n for i in range(len(self.params))]\n vn = math.sqrt(sum(v.pow(2).sum().item() for v in vl))\n if vn > clip_val:\n for v in vl: v.mul_(clip_val / vn)\n for i in range(len(self.params)):\n self.mbuf[i].mul_(self.beta).add_(vl[i])\n self.params[i].data.add_(self.mbuf[i], alpha=-eta)\n nb += 1\n return {\"avg_loss\": total_loss / max(nb, 1), \"full_grad_count\": 1}\n"
7}Tool ResultStep 2
OK: Replaced lines 286..370 with 82 line(s) in opt-vr-bench/custom_vr.py. Editable range: 286–367. [Current file: opt-vr-bench/custom_vr.py | editable: 286–367 | total: 486 lines] 283| 284| 285| # ============================================================================ 286 class VarianceReductionOptimizer: 287 """Momentum-Accelerated SVRG (MA-SVRG). 288 289 Combines SVRG control-variate variance reduction with heavy-ball momentum 290 for accelerated convergence. SVRG cancels stochastic noise via 291 v = g(x)-g(snap)+mu; momentum smooths estimates and provides Polyak-style 292 acceleration on ill-conditioned landscapes. Step is scaled so effective 293 steady-state learning rate equals base_lr. 294 """ 295 296 def __init__(self, model: nn.Module, lr: float, l2_reg: float, 297 loss_type: str, n_train: int, batch_size: int, 298 device: torch.device): 29
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[Test #1] (2 tests remaining; call submit(n=1) to submit this result) ## Seed 42 ### logistic (scripts/logistic.sh) [output file not found: /srv/home/bohanlyu/MLS-Bench/logs/optimization-variance-reduction/anthropic_claude-opus-4.6_20260405_234136/20260405_235635/group_1_0/logistic_s42.out] ### mlp (scripts/mlp.sh) Training progress (last 5 epochs): TRAIN_METRICS: epoch=36 avg_loss=0.323176 time=3.03s grad_comps=28152 TRAIN_METRICS: epoch=37 avg_loss=0.308330 time=3.09s grad_comps=28934 TRAIN_METRICS: epoch=38 avg_loss=0.306290 time=3.04s grad_comps=29716 TRAIN_METRICS: epoch=39 avg_loss=0.294522 time=2.56s grad_comps=30498 TRAIN_METRICS: epoch=40 avg_loss=0.310372 time=1.18s grad_comps=31280 Evaluation progress (last 5 evals): EVAL_METRICS: epoch=32 test_loss=2.495021 test_accuracy=51.120000 best_test_accuracy=52.930000 EVAL_METRICS: epoch=34 test_loss=2.579592 test_accuracy=52.280000 best_test_accuracy=52.930000 EVAL_METRICS: epoch=36 test_loss=2.623234 test_accuracy=51.050000 be
AssistantStep 4edit
Tool Input
1{
2 "op": "replace",
3 "filename": "opt-vr-bench/custom_vr.py",
4 "start_line": 286,
5 "end_line": 367,
6 "content": "class VarianceReductionOptimizer:\n \"\"\"STORM-FR: STORM with per-epoch full-gradient reset.\n\n Novel: resets STORM's running estimate d to the full gradient every\n epoch start (standard STORM only uses full gradient on epoch 1).\n This bounds accumulated drift while preserving STORM's favorable\n within-epoch variance reduction via recursive momentum. Uses\n adaptive step sizing for MSE and gradient clipping for stability.\n \"\"\"\n\n def __init__(self, model: nn.Module, lr: float, l2_reg: float,\n loss_type: str, n_train: int, batch_size: int,\n device: torch.device):\n self.model = model\n self.lr = lr\n self.l2_reg = l2_reg\n self.loss_type = loss_type\n self.n_train = n_train\n self.batch_size = batch_size\n self.device = device\n self.params = list(model.parameters())\n n_steps = max(1, n_train // batch_size)\n self.a = 1.0 - 1.0 / math.sqrt(n_steps)\n self.d = None\n self.prev = None\n self.eta_max = None\n\n def train_one_epoch(self, X_train: torch.Tensor,\n y_train: torch.Tensor) -> dict:\n self.model.train()\n n = X_train.size(0)\n # Reset d to full gradient every epoch (key difference from STORM)\n self.d = compute_full_gradient(\n self.model, X_train, y_train,\n self.loss_type, self.l2_reg, self.device)\n # Adaptive step sizing for ill-conditioned MSE\n gnorm = math.sqrt(sum(g.pow(2).sum().item() for g in self.d))\n pnorm = math.sqrt(sum(\n p.data.pow(2).sum().item() for p in self.params)) + 1e-8\n astep = 0.01 * pnorm / (gnorm + 1e-8)\n if self.loss_type == 'mse':\n if self.eta_max is None: self.eta_max = astep\n else: self.eta_max = min(2.0 * self.eta_max, astep)\n lr_eff = min(self.lr, astep, self.eta_max)\n else:\n lr_eff = self.lr\n clip = max(gnorm * 3.0, 1e-6)\n # prev = current for first step (gc = gp, giving d ≈ full_grad)\n self.prev = [p.data.clone() for p in self.params]\n indices = torch.randperm(n)\n total_loss, nb = 0.0, 0\n for st in range(0, n, self.batch_size):\n end = min(st + self.batch_size, n)\n Xb = X_train[indices[st:end]].to(self.device)\n yb = y_train[indices[st:end]].to(self.device)\n # Gradient at current params + loss tracking\n self.model.zero_grad()\n loss = compute_loss_on_batch(\n self.model, Xb, yb, self.loss_type, self.l2_reg)\n loss.backward()\n gc = [p.grad.clone() for p in self.params]\n self.model.zero_grad()\n total_loss += loss.item()\n # Gradient at previous params (same batch for noise correlation)\n saved = [p.data.clone() for p in self.params]\n for p, pp in zip(self.params, self.prev): p.data.copy_(pp)\n gp = compute_stochastic_gradient(\n self.model, Xb, yb, self.loss_type, self.l2_reg)\n for p, s in zip(self.params, saved): p.data.copy_(s)\n # STORM recursion: d_new = g_curr + a*(d_old - g_prev)\n with torch.no_grad():\n for i in range(len(self.params)):\n self.d[i].sub_(gp[i]).mul_(self.a).add_(gc[i])\n dn = math.sqrt(sum(di.pow(2).sum().item() for di in self.d))\n if dn > clip:\n sc = clip / dn\n for di in self.d: di.mul_(sc)\n self.prev = [p.data.clone() for p in self.params]\n for p, di in zip(self.params, self.d):\n p.data.add_(di, alpha=-lr_eff)\n nb += 1\n return {\"avg_loss\": total_loss / max(nb, 1), \"full_grad_count\": 1}\n"
7}Tool ResultStep 4
OK: Replaced lines 286..367 with 82 line(s) in opt-vr-bench/custom_vr.py. Editable range: 286–367. [Current file: opt-vr-bench/custom_vr.py | editable: 286–367 | total: 486 lines] 283| 284| 285| # ============================================================================ 286 class VarianceReductionOptimizer: 287 """STORM-FR: STORM with per-epoch full-gradient reset. 288 289 Novel: resets STORM's running estimate d to the full gradient every 290 epoch start (standard STORM only uses full gradient on epoch 1). 291 This bounds accumulated drift while preserving STORM's favorable 292 within-epoch variance reduction via recursive momentum. Uses 293 adaptive step sizing for MSE and gradient clipping for stability. 294 """ 295 296 def __init__(self, model: nn.Module, lr: float, l2_reg: float, 297 loss_type: str, n_train: int, batch_size: int, 298 device: torch.
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[Test #2] (1 test remaining; call submit(n=2) to submit this result) ### logistic (scripts/logistic.sh) Training progress (last 5 epochs): TRAIN_METRICS: epoch=16 avg_loss=0.252111 time=1.31s grad_comps=15008 TRAIN_METRICS: epoch=17 avg_loss=0.251490 time=1.28s grad_comps=15946 TRAIN_METRICS: epoch=18 avg_loss=0.250417 time=1.25s grad_comps=16884 TRAIN_METRICS: epoch=19 avg_loss=0.250032 time=1.33s grad_comps=17822 TRAIN_METRICS: epoch=20 avg_loss=0.249464 time=1.35s grad_comps=18760 Evaluation progress (last 5 evals): EVAL_METRICS: epoch=16 test_loss=0.268571 test_accuracy=92.300000 best_test_accuracy=92.570000 EVAL_METRICS: epoch=17 test_loss=0.272069 test_accuracy=92.400000 best_test_accuracy=92.570000 EVAL_METRICS: epoch=18 test_loss=0.268918 test_accuracy=92.440000 best_test_accuracy=92.570000 EVAL_METRICS: epoch=19 test_loss=0.270752 test_accuracy=92.570000 best_test_accuracy=92.570000 EVAL_METRICS: epoch=20 test_loss=0.269597 test_accuracy=92.530000 best_test_accuracy=92.570000
AssistantStep 6edit
Tool Input
1{
2 "op": "replace",
3 "filename": "opt-vr-bench/custom_vr.py",
4 "start_line": 286,
5 "end_line": 367,
6 "content": "class VarianceReductionOptimizer:\n \"\"\"Momentum-Accelerated SVRG (MA-SVRG).\n\n Combines SVRG control-variate variance reduction with heavy-ball\n momentum for accelerated convergence. SVRG cancels stochastic noise\n via v = g(x)-g(snap)+mu; momentum smooths the remaining variance and\n provides Polyak-style acceleration on ill-conditioned landscapes.\n Step is scaled by (1-beta) so effective steady-state lr = base_lr.\n Momentum buffer initialized at steady-state to avoid warm-up lag.\n \"\"\"\n\n def __init__(self, model: nn.Module, lr: float, l2_reg: float,\n loss_type: str, n_train: int, batch_size: int,\n device: torch.device):\n self.model = model\n self.lr = lr\n self.l2_reg = l2_reg\n self.loss_type = loss_type\n self.n_train = n_train\n self.batch_size = batch_size\n self.device = device\n self.params = list(model.parameters())\n self.snap = self.mu = self.mbuf = self.eta_max = None\n self.beta = 0.8\n\n def train_one_epoch(self, X_train: torch.Tensor,\n y_train: torch.Tensor) -> dict:\n self.model.train()\n n = X_train.size(0)\n # Snapshot & full gradient (once per epoch)\n self.snap = [p.data.clone() for p in self.params]\n self.mu = compute_full_gradient(\n self.model, X_train, y_train,\n self.loss_type, self.l2_reg, self.device)\n # Init momentum at steady-state value to avoid warm-up lag\n if self.mbuf is None:\n self.mbuf = [g.clone().div_(1.0 - self.beta) for g in self.mu]\n # Adaptive step sizing (critical for ill-conditioned MSE)\n gnorm = math.sqrt(sum(g.pow(2).sum().item() for g in self.mu))\n pnorm = math.sqrt(sum(\n p.data.pow(2).sum().item() for p in self.params)) + 1e-8\n astep = 0.01 * pnorm / (gnorm + 1e-8)\n if self.loss_type == 'mse':\n if self.eta_max is None: self.eta_max = astep\n else: self.eta_max = min(1.5 * self.eta_max, astep)\n base_lr = min(self.lr, astep, self.eta_max)\n else:\n base_lr = self.lr\n eta = base_lr * (1.0 - self.beta)\n clip_val = max(gnorm * 5.0, 1e-6)\n # Inner SVRG loop with momentum\n indices = torch.randperm(n)\n total_loss, nb = 0.0, 0\n for st in range(0, n, self.batch_size):\n end = min(st + self.batch_size, n)\n Xb = X_train[indices[st:end]].to(self.device)\n yb = y_train[indices[st:end]].to(self.device)\n # Gradient at current params\n self.model.zero_grad()\n loss = compute_loss_on_batch(\n self.model, Xb, yb, self.loss_type, self.l2_reg)\n loss.backward()\n gc = [p.grad.clone() for p in self.params]\n self.model.zero_grad()\n total_loss += loss.item()\n # Gradient at snapshot (same batch for correlated noise cancel)\n saved = [p.data.clone() for p in self.params]\n for p, sp in zip(self.params, self.snap): p.data.copy_(sp)\n gs = compute_stochastic_gradient(\n self.model, Xb, yb, self.loss_type, self.l2_reg)\n for p, s in zip(self.params, saved): p.data.copy_(s)\n # SVRG estimate + gradient clipping + momentum update\n with torch.no_grad():\n vl = [gc[i] - gs[i] + self.mu[i]\n for i in range(len(self.params))]\n vn = math.sqrt(sum(v.pow(2).sum().item() for v in vl))\n if vn > clip_val:\n for v in vl: v.mul_(clip_val / vn)\n for i in range(len(self.params)):\n self.mbuf[i].mul_(self.beta).add_(vl[i])\n self.params[i].data.add_(self.mbuf[i], alpha=-eta)\n nb += 1\n return {\"avg_loss\": total_loss / max(nb, 1), \"full_grad_count\": 1}\n"
7}Tool ResultStep 6
OK: Replaced lines 286..367 with 83 line(s) in opt-vr-bench/custom_vr.py. Editable range: 286–368. [Current file: opt-vr-bench/custom_vr.py | editable: 286–368 | total: 487 lines] 283| 284| 285| # ============================================================================ 286 class VarianceReductionOptimizer: 287 """Momentum-Accelerated SVRG (MA-SVRG). 288 289 Combines SVRG control-variate variance reduction with heavy-ball 290 momentum for accelerated convergence. SVRG cancels stochastic noise 291 via v = g(x)-g(snap)+mu; momentum smooths the remaining variance and 292 provides Polyak-style acceleration on ill-conditioned landscapes. 293 Step is scaled by (1-beta) so effective steady-state lr = base_lr. 294 Momentum buffer initialized at steady-state to avoid warm-up lag. 295 """ 296 297 def __init__(self, model: nn.Module, lr: float, l2_reg: float, 298 loss_type: st
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[Test #3] (0 tests remaining) ## Seed 42 ### logistic (scripts/logistic.sh) Training progress (last 5 epochs): TRAIN_METRICS: epoch=16 avg_loss=0.240142 time=1.54s grad_comps=15008 TRAIN_METRICS: epoch=17 avg_loss=0.239565 time=1.58s grad_comps=15946 TRAIN_METRICS: epoch=18 avg_loss=0.239027 time=1.60s grad_comps=16884 TRAIN_METRICS: epoch=19 avg_loss=0.238462 time=1.74s grad_comps=17822 TRAIN_METRICS: epoch=20 avg_loss=0.237920 time=1.60s grad_comps=18760 Evaluation progress (last 5 evals): EVAL_METRICS: epoch=16 test_loss=0.265867 test_accuracy=92.550000 best_test_accuracy=92.580000 EVAL_METRICS: epoch=17 test_loss=0.265940 test_accuracy=92.540000 best_test_accuracy=92.580000 EVAL_METRICS: epoch=18 test_loss=0.266042 test_accuracy=92.560000 best_test_accuracy=92.580000 EVAL_METRICS: epoch=19 test_loss=0.266170 test_accuracy=92.570000 best_test_accuracy=92.580000 EVAL_METRICS: epoch=20 test_loss=0.266257 test_accuracy=92.570000 best_test_accuracy=92.580000 Final metrics (logistic):