Reinforcement Learning as MDP

Reinforcement Learning Approaches

Model-based Reinforcement Learning

PILCO [Deisenroth et al. 2011]

PETS [Chua et al. 2018]

Chua, K.; Calandra, R.; McAllister, R. & Levine, S.
Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models
Advances in Neural Information Processing Systems (NIPS), 2018, 4754-4765

Experimental Results

Is Something Strange about MBRL?

How to Use the Reward?

Goal-Driven Dynamics Learning

• Instead of optimizing the forward dynamics w.r.t. the NLL of the next state, we optimize w.r.t. the reward
  (The reward is all we care about)
   
• Computing the gradients analytically is intractable
   
• We use a zero-order optimizer: Bayesian optimization
   
• (and an LQG framework)

Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
Goal-Driven Dynamics Learning via Bayesian Optimization
IEEE Conference on Decision and Control (CDC), 2017, 5168-5173

Real-world Quadcopter

Dubins Car

Conclusion

There exist models that are wrong, but nearly optimal when used for control

• From a Sys.ID perspective, they are completely wrong
• These models might be out-of-class (e.g., linear model for non-linear dynamics)
• Hyphothesis: these models capture some structure of the optimal solution, ignoring the rest of the space
• Evidence: these models do not seem to generalize to new tasks

All models are wrong, but some are useful

- George E.P. Box

If wrong models can be useful,
Can correct models be useless?

Model Likelihood vs Episode Reward

Objective Mismatch

Objective mismatch arises when one objective is optimized in the hope that a second, often uncorrelated, metric will also be optimized.

Likelihood vs Reward

Deterministic model

Probabilistic model

Assumption: Optimizing the likelihood will optimize the reward

System Identification

Model-based Reinforcement Learning

Sys ID vs MBRL

Objective Mismatch

Experimental results show that the likelihood of the trained models are not strongly correlated with task performance

What are the consequences?

Adversarially Generated Dynamics

What can we do?

• Modify objective when training dynamics model
  • add controllability regularization [Singh et al. 2019]
  • end-to-end differentiable models [Amos et al. 2019]
  • ...
• Move away from the single-task formulation
• ???

Re-weighted Likelihood

How can we give more importance to data that are important for the specific task at hand?

Overview

Introduced and analyzed Objective Mismatch in MBRL

• Identify fundamental flaw of current approach
• Provides new lens to understand MBRL
• Open exciting new venues

References

• Deisenroth, M.; Fox, D. & Rasmussen, C.
  Gaussian Processes for Data-Efficient Learning in Robotics and Control
  IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 2014, 37, 408-423
• Chua, K.; Calandra, R.; McAllister, R. & Levine, S.
  Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models
  Advances in Neural Information Processing Systems (NIPS), 2018, 4754-4765
• Tian, S.; Ebert, F.; Jayaraman, D.; Mudigonda, M.; Finn, C.; Calandra, R. & Levine, S.
  Manipulation by Feel: Touch-Based Control with Deep Predictive Models
  IEEE International Conference on Robotics and Automation (ICRA), 2019
• Lambert, N.O.; Drew, D.S.; Yaconelli, J; Calandra, R.; Levine, S.; & Pister, K.S.J.
  Low Level Control of a Quadrotor with Deep Model-Based Reinforcement Learning
  IEEE Robotics and Automation Letters (RA-L), 2019, 4, 4224-4230

• Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
  Goal-Driven Dynamics Learning via Bayesian Optimization
  IEEE Conference on Decision and Control (CDC), 2017, 5168-5173

• Lambert, N.; Amos, B.; Yadan, O. & Calandra, R.

  Objective Mismatch in Model-based Reinforcement Learning
  Under review, Soon on Arxiv, 2019

Motivation

Learning to Fly a Quadcopter

Lambert, N.O.; Drew, D.S.; Yaconelli, J; Calandra, R.; Levine, S.; & Pister, K.S.J.
Low Level Control of a Quadrotor with Deep Model-Based Reinforcement Learning
IEEE Robotics and Automation Letters (RA-L), 2019, 4, 4224-4230

Ablation Study

Design Choices in MBRL

• Dynamics Model
  • Forward dynamics
    (Most used nowadays, since it is independent from the task and is causal, therefore allowing proper uncertainty propagation!)
  • What model to use? (Gaussian process, neural network, etc)

• How to compute long-term predictions?
  • Usually, recursive propagation in the state-action space
  • Error compounds multiplicatively
  • How do we propagate uncertainty?

• What planner/policy to use?
  • Training offline parametrized policy
  • or using online Model Predictive Control (MPC)