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AutoML systems fundamentally trade compute resources for human expertise. This trade has economics: compute costs money, takes time, and consumes energy. Understanding how to allocate resources efficiently is essential for extracting maximum value from AutoML investments.
Resource budgeting in AutoML is not simply a matter of 'run until resources are exhausted.' Sophisticated budget management involves understanding the diminishing returns curve, implementing intelligent stopping criteria, allocating resources across search phases, and balancing the exploration-exploitation tradeoff. This page provides the comprehensive framework for mastering AutoML resource economics.
By the end of this page, you will understand how to allocate compute budgets strategically, set effective time limits, implement early stopping mechanisms, optimize cost-performance tradeoffs, and apply progressive resource allocation strategies that maximize model quality within real-world constraints.
The relationship between resources invested and model performance follows a characteristic pattern that every AutoML practitioner must understand. This pattern exhibits diminishing returns—initial resource investment yields substantial gains, but additional resources provide progressively smaller improvements.
The Four Phases of AutoML Search:
Phase 1: Rapid Improvement (0-20% of budget)
Phase 2: Refinement (20-60% of budget)
Phase 3: Diminishing Returns (60-90% of budget)
Phase 4: Plateau/Overfitting Risk (>90% of budget)
In practice, most AutoML problems exhibit an 80/20 pattern: 80% of achievable performance gain occurs in the first 20% of the resource budget. The remaining 80% of resources contribute only 20% of performance improvement. Understanding this curve is critical for efficient resource allocation.
| Budget % | Cumulative Performance % | Marginal ROI | Recommended Action |
|---|---|---|---|
| 0-10% | 50-60% | Very High | Always invest |
| 10-25% | 70-80% | High | Standard investment |
| 25-50% | 85-92% | Medium | Continue for production quality |
| 50-75% | 94-97% | Low | Only for high-stakes applications |
| 75-100% | 97-99% | Very Low | Rarely justified |
100% | 99-100% | Near Zero | Wasteful; risk of overfitting |
Compute budget encompasses the computational resources allocated to AutoML search, measured in CPU/GPU hours, wall-clock time, or cloud cost. Effective allocation requires understanding both the total budget available and how to distribute that budget across search components.
Budget Sizing Guidelines:
Determining the right total budget depends on problem characteristics:
| Dataset Size | Problem Complexity | Minimum Budget | Recommended Budget | Extended Budget |
|---|---|---|---|---|
| Small (<10K rows) | Simple (tabular, standard features) | 1 CPU-hour | 4-8 CPU-hours | 24 CPU-hours |
| Medium (10K-1M rows) | Moderate (engineered features, imbalanced) | 4 CPU-hours | 24-48 CPU-hours | 100 CPU-hours |
| Large (1M-100M rows) | Complex (many features, high cardinality) | 24 CPU-hours | 100-500 CPU-hours | 1000+ CPU-hours |
| Very Large (>100M rows) | Very Complex (deep learning, NAS) | 100 GPU-hours | 500-2000 GPU-hours | 10000+ GPU-hours |
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def estimate_automl_budget( dataset_rows: int, num_features: int, problem_type: str, cv_folds: int = 5, algorithms_to_search: int = 20, hyperparameter_trials_per_algo: int = 50) -> dict: """ Estimate AutoML compute budget based on problem characteristics. Returns estimates in CPU-hours for tabular problems. For deep learning/NAS, multiply by ~10-100x and consider GPU requirements. """ # Base training time estimates (seconds per 1000 rows) BASE_TRAINING_TIMES = { 'linear': 0.1, # LogisticRegression, Ridge, Lasso 'tree': 0.5, # DecisionTree 'ensemble': 2.0, # RandomForest, XGBoost, LightGBM 'svm': 5.0, # SVMs (scales poorly with data size) 'neural': 10.0, # Small MLPs } # Estimate base training time per model avg_training_time_per_1k = sum(BASE_TRAINING_TIMES.values()) / len(BASE_TRAINING_TIMES) base_training_seconds = (dataset_rows / 1000) * avg_training_time_per_1k # Scale by features (roughly sqrt relationship) feature_multiplier = (num_features / 50) ** 0.5 scaled_training_seconds = base_training_seconds * feature_multiplier # Total evaluations total_evaluations = algorithms_to_search * hyperparameter_trials_per_algo * cv_folds # Total compute in seconds total_seconds = scaled_training_seconds * total_evaluations # Convert to hours cpu_hours = total_seconds / 3600 return { 'estimated_cpu_hours': round(cpu_hours, 1), 'minimum_budget': round(cpu_hours * 0.25, 1), 'recommended_budget': round(cpu_hours, 1), 'extended_budget': round(cpu_hours * 3, 1), 'total_evaluations': total_evaluations, 'avg_seconds_per_eval': round(scaled_training_seconds, 2), } # Example usagebudget = estimate_automl_budget( dataset_rows=100_000, num_features=100, problem_type='classification', cv_folds=5, algorithms_to_search=15, hyperparameter_trials_per_algo=40) print(f"Estimated CPU-hours: {budget['estimated_cpu_hours']}")print(f"Recommended budget: {budget['recommended_budget']} CPU-hours")print(f"Total evaluations planned: {budget['total_evaluations']}")To convert CPU-hours to cloud costs: AWS EC2 c5.xlarge (4 vCPU) costs ~$0.17/hour. A 100 CPU-hour budget ≈ 25 instance-hours ≈ $4.25 on-demand or ~$1.50 with spot instances. GPU instances (p3.2xlarge) cost ~$3/hour. Budget accordingly.
Time budgets constrain AutoML by wall-clock duration rather than compute consumption. This is often the more practical constraint in real-world projects where deadlines matter more than compute costs. Effective time budgeting requires understanding how time maps to search progress.
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# Auto-sklearn: Time budget configurationfrom autosklearn.classification import AutoSklearnClassifier # Strategy 1: Fixed total time limitclf_fixed = AutoSklearnClassifier( time_left_for_this_task=3600, # Total time: 1 hour per_run_time_limit=300, # Max 5 minutes per model ensemble_size=20, ensemble_nbest=10, memory_limit=8192, # 8GB RAM limit) # Strategy 2: Aggressive early stopping for quick iterationclf_quick = AutoSklearnClassifier( time_left_for_this_task=600, # 10 minutes total per_run_time_limit=60, # Max 1 minute per model initial_configurations_via_metalearning=10, # Warm start ensemble_size=5,) # Strategy 3: Extended search for production qualityclf_production = AutoSklearnClassifier( time_left_for_this_task=14400, # 4 hours total per_run_time_limit=600, # 10 minutes per model ensemble_size=50, ensemble_nbest=25, resampling_strategy='cv', resampling_strategy_arguments={'folds': 5},) # AutoGluon: Preset-based time allocationfrom autogluon.tabular import TabularPredictor # Quick prototypingpredictor_quick = TabularPredictor(label='target').fit( train_data, time_limit=300, # 5 minutes presets='medium_quality',) # Production-readypredictor_prod = TabularPredictor(label='target').fit( train_data, time_limit=3600, # 1 hour presets='best_quality', auto_stack=True,) # Custom per-model limits with AutoGluonpredictor_custom = TabularPredictor(label='target').fit( train_data, time_limit=7200, # 2 hours total hyperparameters={ 'GBM': {'num_boost_round': 10000, 'ag_args_fit': {'max_time_limit': 600}}, 'NN_TORCH': {'epochs': 100, 'ag_args_fit': {'max_time_limit': 1200}}, 'CAT': {'iterations': 5000, 'ag_args_fit': {'max_time_limit': 600}}, },)Time Allocation Heuristics:
When setting time budgets, consider these empirically-validated heuristics:
| Dataset Size | Minimum Meaningful Budget | Standard Budget | Extended Budget |
|---|---|---|---|
| <10K rows | 5-10 minutes | 30-60 minutes | 2-4 hours |
| 10K-100K rows | 30-60 minutes | 2-4 hours | 8-24 hours |
| 100K-1M rows | 2-4 hours | 8-24 hours | 2-7 days |
1M rows | 8-24 hours | 2-7 days | 2-4 weeks |
These budgets assume availability of multi-core CPUs. GPU acceleration can reduce deep learning components by 10-50x but doesn't affect tree-based methods.
Always set per-model time limits in addition to total time limits. Without per-model limits, a single pathological configuration (e.g., SVM with RBF kernel on large data) can consume your entire budget, leaving most algorithms unexplored.
Early stopping is the process of terminating AutoML search before the allocated budget is exhausted when further search is unlikely to improve results. Effective early stopping dramatically improves resource efficiency without sacrificing model quality.
Successive Halving and Hyperband:
Successive Halving is one of the most effective early stopping strategies for hyperparameter optimization. The approach is elegantly simple:
Mathematical Formulation:
Given total budget B and n initial configurations:
This achieves logarithmic speedup over grid search while maintaining quality guarantees.
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import numpy as npfrom typing import List, Callable class SuccessiveHalving: """ Successive Halving for hyperparameter optimization. Efficiently allocates budget by progressively eliminating poorly performing configurations. """ def __init__( self, total_budget: int, num_configs: int, reduction_factor: int = 3, min_budget_per_config: int = 1 ): """ Args: total_budget: Total compute budget (e.g., epochs, iterations) num_configs: Number of initial configurations to evaluate reduction_factor: Fraction of configs to keep each round (default: keep 1/3) min_budget_per_config: Minimum budget for first round """ self.total_budget = total_budget self.num_configs = num_configs self.reduction_factor = reduction_factor self.min_budget = min_budget_per_config # Calculate schedule self.schedule = self._compute_schedule() def _compute_schedule(self) -> List[dict]: """Compute the successive halving schedule.""" schedule = [] n_configs = self.num_configs budget = self.min_budget while n_configs >= 1: schedule.append({ 'num_configs': int(n_configs), 'budget_per_config': int(budget), }) n_configs = n_configs / self.reduction_factor budget = budget * self.reduction_factor return schedule def run( self, configs: List[dict], evaluate_fn: Callable[[dict, int], float], ) -> dict: """ Run successive halving. Args: configs: List of configurations to evaluate evaluate_fn: Function(config, budget) -> score (higher is better) Returns: Best configuration found """ active_configs = configs[:self.num_configs] for round_idx, round_info in enumerate(self.schedule): budget = round_info['budget_per_config'] n_to_keep = round_info['num_configs'] print(f"Round {round_idx}: Evaluating {len(active_configs)} configs " f"with budget {budget}") # Evaluate all active configurations scores = [] for config in active_configs: score = evaluate_fn(config, budget) scores.append((score, config)) # Sort by score (descending) and keep top performers scores.sort(key=lambda x: x[0], reverse=True) active_configs = [cfg for _, cfg in scores[:n_to_keep]] print(f" Best score this round: {scores[0][0]:.4f}") return active_configs[0] if active_configs else None class SearchLevelEarlyStopping: """ Early stopping for the overall AutoML search based on improvement history. """ def __init__( self, patience: int = 20, min_improvement: float = 0.001, min_evaluations: int = 50, ): """ Args: patience: Number of evaluations without improvement before stopping min_improvement: Minimum relative improvement to count as progress min_evaluations: Minimum evaluations before early stopping is considered """ self.patience = patience self.min_improvement = min_improvement self.min_evaluations = min_evaluations self.best_score = float('-inf') self.evaluations_since_improvement = 0 self.total_evaluations = 0 self.history = [] def update(self, score: float) -> bool: """ Update with new evaluation result. Returns: True if search should continue, False if should stop """ self.total_evaluations += 1 self.history.append(score) # Check for improvement relative_improvement = (score - self.best_score) / max(abs(self.best_score), 1e-10) if relative_improvement > self.min_improvement: self.best_score = score self.evaluations_since_improvement = 0 else: self.evaluations_since_improvement += 1 # Decide whether to continue if self.total_evaluations < self.min_evaluations: return True # Keep searching if self.evaluations_since_improvement >= self.patience: print(f"Early stopping: No improvement for {self.patience} evaluations") return False # Stop searching return True # Keep searching def get_statistics(self) -> dict: """Get search statistics.""" return { 'total_evaluations': self.total_evaluations, 'best_score': self.best_score, 'evaluations_since_improvement': self.evaluations_since_improvement, 'improvement_rate': len([h for h in self.history if h >= self.best_score * 0.99]) / max(len(self.history), 1), } # Usage exampledef example_usage(): # Successive Halving example sh = SuccessiveHalving( total_budget=1000, num_configs=81, reduction_factor=3, min_budget_per_config=10 ) print("Successive Halving Schedule:") for i, round_info in enumerate(sh.schedule): print(f" Round {i}: {round_info['num_configs']} configs, " f"{round_info['budget_per_config']} budget each") # Early stopping example stopper = SearchLevelEarlyStopping(patience=10, min_evaluations=30) # Simulate search with diminishing returns for i in range(100): # Simulate score that improves initially then plateaus score = 0.5 + 0.4 * (1 - np.exp(-i/10)) + np.random.normal(0, 0.01) if not stopper.update(score): print(f"Stopped at evaluation {i}") break print(f"Final stats: {stopper.get_statistics()}")A practical rule of thumb: if the top-5 models haven't improved by more than 0.1% for 20 consecutive evaluations after at least 50 total evaluations, further search is typically wasteful. This heuristic works well across diverse tabular problems.
Multi-fidelity optimization exploits the insight that cheap approximations can identify promising configurations before expensive full evaluations. By evaluating on subsets of data, fewer epochs, or simpler proxies, multi-fidelity methods dramatically accelerate AutoML search.
Key Fidelity Dimensions:
1. Data Subsampling
2. Epoch/Iteration Reduction
3. Model Simplification
4. Cross-Validation Reduction
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import numpy as npfrom sklearn.model_selection import cross_val_scorefrom sklearn.ensemble import RandomForestClassifierfrom typing import Dict, Any, Tuple class MultiFidelityOptimizer: """ Multi-fidelity hyperparameter optimization using data subsampling. Evaluates configurations on progressively larger data subsets, eliminating poorly performing configurations early. """ def __init__( self, fidelity_levels: list = [0.1, 0.3, 0.5, 1.0], survival_rate: float = 0.5, cv_folds: int = 3, ): """ Args: fidelity_levels: Data fraction at each stage (increasing) survival_rate: Fraction of configs that survive each round cv_folds: Cross-validation folds for evaluation """ self.fidelity_levels = fidelity_levels self.survival_rate = survival_rate self.cv_folds = cv_folds def _subsample(self, X, y, fraction: float): """Subsample data to given fraction.""" n_samples = int(len(X) * fraction) indices = np.random.choice(len(X), n_samples, replace=False) return X[indices], y[indices] def _evaluate_config( self, config: Dict[str, Any], X, y, fidelity: float ) -> float: """Evaluate a configuration at given fidelity level.""" X_sub, y_sub = self._subsample(X, y, fidelity) model = RandomForestClassifier(**config, random_state=42) scores = cross_val_score(model, X_sub, y_sub, cv=self.cv_folds) return scores.mean() def optimize( self, configs: list, X, y, ) -> Tuple[Dict[str, Any], float]: """ Run multi-fidelity optimization. Args: configs: List of configuration dicts X: Feature matrix y: Target vector Returns: Tuple of (best_config, best_score) """ active_configs = configs.copy() for fidelity in self.fidelity_levels: n_survive = max(1, int(len(active_configs) * self.survival_rate)) print(f"Fidelity {fidelity:.0%}: Evaluating {len(active_configs)} configs") # Evaluate all active configs results = [] for config in active_configs: score = self._evaluate_config(config, X, y, fidelity) results.append((score, config)) # Sort and keep top performers results.sort(key=lambda x: x[0], reverse=True) # Report top score at this fidelity print(f" Top score at {fidelity:.0%} fidelity: {results[0][0]:.4f}") # Keep survivors for next round active_configs = [cfg for _, cfg in results[:n_survive]] # Final result is best config at full fidelity return active_configs[0], results[0][0] # Example: Hyperband implementation sketchclass Hyperband: """ Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization. Combines successive halving with multiple brackets to handle the exploration-exploitation tradeoff in budget allocation. """ def __init__( self, max_budget: int, reduction_factor: float = 3, ): self.max_budget = max_budget # R in paper self.eta = reduction_factor # η in paper # Number of successive halving brackets self.s_max = int(np.log(max_budget) / np.log(reduction_factor)) self.B = (self.s_max + 1) * max_budget # Total budget def get_brackets(self) -> list: """ Generate Hyperband brackets. Each bracket represents a successive halving run with different initial configurations and budgets. """ brackets = [] for s in range(self.s_max, -1, -1): # Number of configurations in this bracket n = int(np.ceil((self.B / self.max_budget) * (self.eta ** s) / (s + 1))) # Minimum budget per config in this bracket r = self.max_budget * (self.eta ** (-s)) bracket = { 'bracket_id': self.s_max - s, 'initial_configs': n, 'min_budget': r, 'num_rounds': s + 1, } brackets.append(bracket) return brackets def print_schedule(self): """Print Hyperband schedule for visualization.""" print(f"Hyperband Schedule (max_budget={self.max_budget}, η={self.eta})") print(f"Total budget per run: {self.B}") print() for bracket in self.get_brackets(): print(f"Bracket {bracket['bracket_id']}:") print(f" Initial configs: {bracket['initial_configs']}") print(f" Minimum budget: {bracket['min_budget']:.1f}") print(f" Rounds: {bracket['num_rounds']}") # Show successive halving within bracket n = bracket['initial_configs'] r = bracket['min_budget'] for round_idx in range(bracket['num_rounds']): print(f" Round {round_idx}: {int(n)} configs × {int(r)} budget") n = n / self.eta r = r * self.eta print() # Demoif __name__ == "__main__": hb = Hyperband(max_budget=81, reduction_factor=3) hb.print_schedule()Multi-fidelity optimization works best when low-fidelity evaluations are predictive of high-fidelity performance. This assumption holds for most neural networks and gradient boosting but may fail for models where performance is non-monotonic in resources (e.g., some regularization settings).
For cloud-based AutoML, monetary cost becomes a primary concern. Cost optimization requires understanding cloud pricing models and tailoring AutoML strategies accordingly.
| Strategy | Hourly Cost (Example) | Reliability | Best For |
|---|---|---|---|
| On-Demand Instances | $1.00/CPU-hour | High | Critical production runs |
| Spot/Preemptible | $0.30/CPU-hour | Medium (interruptions) | Experimentation, long runs |
| Reserved (1-year) | $0.60/CPU-hour | High | Regular pipeline runs |
| Managed AutoML (Vertex, SageMaker) | $0.50-2.00/model-hour | Very High | Low operational overhead |
| Hybrid (Spot + On-Demand fallback) | $0.40/CPU-hour average | High | Cost-sensitive production |
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"""Cost-Aware AutoML Configuration Examples""" # AWS SageMaker Autopilot with cost controlsimport sagemakerfrom sagemaker.automl.automl import AutoML automl = AutoML( role='SageMakerRole', target_attribute_name='target', output_path='s3://bucket/output', # Cost control: limit job duration max_runtime_per_training_job_in_seconds=600, total_job_runtime_in_seconds=7200, # Cost control: limit candidates max_candidates=50, # Use spot instances for training problem_type='BinaryClassification', job_objective={'MetricName': 'AUC'},) # Google Cloud Vertex AI with budget constraintsfrom google.cloud import aiplatform aiplatform.init(project='my-project', location='us-central1') # Create AutoML job with budget awarenessjob = aiplatform.AutoMLTabularTrainingJob( display_name='cost-aware-automl', optimization_prediction_type='classification', optimization_objective='maximize-au-roc',) model = job.run( dataset=dataset, target_column='target', # Budget constraints budget_milli_node_hours=1000, # 1 node-hour maximum # Disable neural architecture search to reduce cost disable_early_stopping=False,) # H2O AutoML with resource limitsimport h2ofrom h2o.automl import H2OAutoML h2o.init(max_mem_size='8G') # Limit memory aml = H2OAutoML( max_runtime_secs=3600, # 1 hour limit max_models=20, # Model limit # Exclude expensive algorithm families to control cost exclude_algos=['DeepLearning'], # Skip neural networks # Use less cross-validation nfolds=3, # 3-fold instead of default 5 # Early stopping stopping_metric='AUC', stopping_rounds=5, stopping_tolerance=0.001,) aml.train(x=features, y=target, training_frame=train) def estimate_cloud_cost( cpu_hours: float, gpu_hours: float = 0, storage_gb_months: float = 10, instance_type: str = 'spot') -> dict: """ Estimate cloud costs for AutoML run. Based on approximate AWS pricing (varies by region/time). """ PRICES = { 'cpu_ondemand': 0.17, # per vCPU-hour 'cpu_spot': 0.05, # per vCPU-hour 'cpu_reserved': 0.10, # per vCPU-hour 'gpu_ondemand': 3.06, # per GPU-hour (V100) 'gpu_spot': 0.90, # per GPU-hour 'storage': 0.023, # per GB-month (S3) } if instance_type == 'spot': cpu_cost = cpu_hours * PRICES['cpu_spot'] gpu_cost = gpu_hours * PRICES['gpu_spot'] elif instance_type == 'reserved': cpu_cost = cpu_hours * PRICES['cpu_reserved'] gpu_cost = gpu_hours * PRICES['gpu_ondemand'] * 0.6 # ~40% discount else: # on-demand cpu_cost = cpu_hours * PRICES['cpu_ondemand'] gpu_cost = gpu_hours * PRICES['gpu_ondemand'] storage_cost = storage_gb_months * PRICES['storage'] total = cpu_cost + gpu_cost + storage_cost return { 'cpu_cost': round(cpu_cost, 2), 'gpu_cost': round(gpu_cost, 2), 'storage_cost': round(storage_cost, 2), 'total_cost': round(total, 2), 'instance_type': instance_type, } # Exampleprint(estimate_cloud_cost(cpu_hours=100, gpu_hours=10, instance_type='spot'))# {'cpu_cost': 5.0, 'gpu_cost': 9.0, 'storage_cost': 0.23, 'total_cost': 14.23, 'instance_type': 'spot'}Spot instances are ideal for AutoML because: (1) AutoML is naturally fault-tolerant—interrupted evaluations can restart, (2) most evaluations are independent, enabling easy rescheduling, (3) checkpointing allows resumption mid-training. Configure your AutoML to save checkpoints every 10-15 minutes to minimize waste from interruptions.
Organizations running multiple AutoML projects must allocate a finite budget across projects. This portfolio perspective requires balancing exploration (trying new approaches) with exploitation (refining known successes).
Portfolio Allocation Principles:
1. Prioritize by Business Impact Allocate more budget to projects with higher potential business value. A 1% improvement on a $100M revenue stream justifies more investment than a 10% improvement on a $100K stream.
2. Consider Marginal Returns Projects early in development have higher marginal returns from additional budget than mature projects near performance plateaus.
3. Diversify Risk Don't concentrate all budget on a single speculative project. Spread allocation to ensure some projects definitely succeed.
4. Reserve Contingency Maintain 10-20% budget reserve for unexpected opportunities or project extensions. AutoML often reveals promising directions that warrant further exploration.
| Project | Business Value | Current Stage | Marginal ROI | Budget % |
|---|---|---|---|---|
| Customer Churn | High ($5M/yr impact) | Development | High | 30% |
| Fraud Detection | Critical (risk mitigation) | Refinement | Medium | 25% |
| Pricing Optimization | High ($3M/yr impact) | Exploration | Very High | 20% |
| Inventory Forecasting | Medium ($500K/yr impact) | Production | Low | 10% |
| Customer Segmentation | Medium (strategic) | Development | High | 10% |
| Contingency Reserve | — | — | — | 5% |
A useful heuristic for AutoML portfolio allocation: 70% to proven, production-critical models with clear ROI; 20% to promising development projects with high potential; 10% to speculative exploration of new problem areas or techniques. This balance ensures both reliability and innovation.
We've covered the comprehensive landscape of AutoML resource budgeting. Let's consolidate the essential principles:
What's Next:
With resource budgeting mastered, we turn to a critical operational challenge: Constraint Handling. The next page examines how to incorporate real-world constraints—latency requirements, memory limits, fairness criteria, regulatory requirements—into AutoML search to produce models that are not just accurate but deployable.
You now have a comprehensive framework for AutoML resource budgeting—from individual search runs to organizational portfolio allocation. This knowledge enables efficient investment of compute resources, avoiding both under-exploration and wasteful over-search.