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notes about mppi guided policy search

  1. The Exploration Challenge
  • Pure policy learning struggles with exploration in complex action spaces
  • Random actions rarely stumble upon useful behaviors in non-trivial tasks
  • The space of potentially useful trajectories is tiny compared to the space of all possible trajectories
  1. The Trajectory Optimization Advantage
  • Model-based trajectory optimization can more efficiently find valid solutions
  • It can use gradient information through the dynamics model
  • While computationally expensive per trajectory, it can find solutions that would take policy learning "forever" to discover
  1. The Policy Learning Benefits
  • Policies are fast to evaluate once trained
  • They can generalize across states
  • More practical for real-time control
  1. The Synthesis
  • Using trajectory optimization to generate demonstrations transforms RL into supervised learning
  • The policy can learn from "perfect" demonstrations that are already adapted to its own dynamics
  • This sidesteps the correspondence problem you'd have using human or other-robot demonstrations

techniques like DAGGER (Dataset Aggregation) and guided policy learning, but with trajectory optimization as the expert rather than a human demonstrator. You're essentially using the computationally expensive but more capable trajectory optimizer as a teacher for the faster but initially clueless policy.

the main challenge then becomes selecting which trajectories to generate to provide the most useful training data for the policy Since even though trajectory optimization is better than random exploration, it's still too expensive to generate exhaustive coverage of the state space.

MPPI Guided Policy Learning

Core Intuition

Policy learning for complex systems faces a fundamental challenge: exploration is hard. The core problem in reinforcement learning isn't really about learning - it's about exploration. Traditional policy learning methods struggle because:

  1. Random exploration rarely finds useful behaviors in high-dimensional spaces
  2. The policy needs to both explore and exploit, which creates conflicting objectives
  3. Getting initial examples of successful behavior is extremely difficult

The Solution: Model-Based Trajectory Optimization

Instead of hoping a policy stumbles upon good behaviors, we can use model-based trajectory optimization (like MPPI) to:

  • Actively plan sequences of actions that achieve the task
  • Leverage known dynamics models
  • Use parallel sampling to explore efficiently
  • Optimize over shorter horizons where planning is more tractable

Key Insight: Bridging Trajectory Optimization and Policy Learning

Rather than treating them as separate approaches, we can combine their strengths:

  1. MPPI provides demonstrations of successful behavior
  2. The policy learns from these demonstrations via supervised learning
  3. The policy can then provide better initialization for MPPI
  4. This creates a virtuous cycle of improvement

Advantages

  1. Better Exploration:

    • MPPI can efficiently explore using parallel sampling
    • The policy learns from successful trajectories rather than random exploration
    • Coverage of state space can be controlled through MPPI initialization

  2. Computational Efficiency:

    • MPPI handles the expensive planning during training
    • The final policy is fast to evaluate
    • Policy can smooth out aggressive MPPI behaviors

  3. Sample Efficiency:

    • Every MPPI rollout provides learning signal
    • Failed trajectories still provide useful information
    • Can leverage all sampled trajectories, not just the optimal one

  4. Practical Benefits:

    • Turns RL into supervised learning
    • Easier to debug and understand
    • More stable training process
    • Can incorporate demonstrations naturally

Implementation Details

MPPI Component

  • Samples multiple trajectory rollouts
  • Uses importance sampling to weight trajectories
  • Can be temperature-tuned for exploration/exploitation
  • Benefits from parallel computation

Policy Component

  • Can be any function approximator (neural net, linear, etc.)
  • Learns via supervised regression on MPPI actions
  • Provides fast inference at runtime
  • Smooths out aggressive MPPI behaviors

Training Loop

  1. Initialize state
  2. Run MPPI to get optimal trajectory
  3. Update policy to match MPPI actions
  4. Use updated policy to initialize next MPPI optimization
  5. Repeat

Extensions

  1. Demonstration Integration:

    • MPPI can follow demonstrations more easily than direct policy learning
    • Can mix demonstration data with MPPI trajectories
    • Provides smooth interpolation between demos

  2. Modified MPPI:

    • Can adapt MPPI for specific tasks
    • Policy still learns via supervised learning
    • Allows for task-specific optimization tricks

  3. Multi-Task Learning:

    • Can generate data for multiple tasks
    • Policy can learn to generalize across tasks
    • MPPI handles exploration for each task

Common Challenges

  1. Distribution Mismatch:

    • MPPI trajectories may not match ideal policy distribution
    • Need to ensure policy can reproduce MPPI behavior
    • May need to add noise or regularization

  2. Horizon Effects:

    • MPPI works best with shorter horizons
    • Policy needs to learn longer-term behavior
    • May need curriculum learning for complex tasks

  3. Model Error:

    • MPPI relies on accurate dynamics model
    • Policy may learn to compensate for model errors
    • Need robust cost functions

Best Practices

  1. Start with short horizons and gradually increase
  2. Use temperature annealing in MPPI
  3. Include state diversity in cost function
  4. Monitor policy vs MPPI performance gap
  5. Use ensemble of policies for uncertainty estimation