Theory and Practice of
Modelbased Reinforcement Learning
Roberto Calandra
Caltech  CS 159  25 May 2021
Facebook AI Research
Towards Artificial Agents in the Wild
How to scale to more complex, unstructured domains?
Robotics
Finance
Biological Sciences
Logistics /
Decision Making
Why Robots?
Disaster Relief
Industrial Automation
Exploration
Medicine & Eldercare
State of the Art in Robotics
From YouTube: https://www.youtube.com/watch?v=g0TaYhjpOfo
What are we missing?
Key Challenges

Multimodal Sensing

Optimized Hardware Design

Quick adaptation to new tasks
Touch Sensing
Morphological adaptation
In this talk
Modelbased
Reinforcement Learning
Hardware
Software
Learning Models of the World for Fast Adaptation of Motor Skills
PILCO [Deisenroth et al. 2011]
Learning Models of the World
Humans seem to make extensive use of predictive models for planning and control *
(e.g., to predict the effects of our actions)
Can artificial agents learn and use predictive models of the world?
Hyphothesis: better predictive capabilities will lead to more efficient adaptation
* [Kawato, M. Internal models for motor control and trajectory planning Current Opinion in Neurobiology , 1999, 9, 718  727],
[Gläscher, J.; Daw, N.; Dayan, P. & O'Doherty, J. P. States versus rewards: dissociable neural prediction error signals underlying modelbased and modelfree reinforcement
learning Neuron, Elsevier, 2010, 66, 585595]
+
predictive models enable explainability
(by peeking into the beliefs of our models and understand their decisions)
Reinforcement Learning Approaches
Modelfree:

Local convergence guaranteed*

Simple to implement

Computationally light

Does not generalize

Datainefficient
Modelbased:

No convergence guarantees

Challenging to learn model

Computationally intensive

Dataefficient

Generalize to new tasks
Evidence from neuroscience that humans use both approaches! [Daw et al. 2010]
Modelbased Reinforcement Learning
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)
 Forward dynamics

How to compute longterm predictions?
 Usually, recursive propagation in the stateaction 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)
PILCO [Deisenroth et al. 2011]
 Gaussian Process (GP) for the forward dynamics model
 Propagates uncertainty over state and action by using Moment Matching  this approximation allows an analytical solution for the derivatives
 Directly optimizes a closedform policy (e.g., RBF network) by backpropagating the reward through the trajectory to the policy parameters
(Gradients can be computed easily by chain rule) and using a firstorder optimizer.  Reward function needs to be know in an analytical form
Probabilistic Ensembles with Trajectory Sampling (PETS)
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, 47544765
Experimental Results
1000x
Faster than
Modelfree RL
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, 47544765
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, 47544765
Is Something Strange about MBRL?
How to Use the Reward?
GoalDriven 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 used a zeroorder optimizer: e.g., Bayesian optimization
 (and an LQG framework)
Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
GoalDriven Dynamics Learning via Bayesian Optimization
IEEE Conference on Decision and Control (CDC), 2017, 51685173
Realworld Quadcopter
Dubins Car
Not the only way to use the Reward
Bansal, S.; Calandra, R.; Levine, S. & Tomlin, C. J.
MBMF: ModelBased Priors for ModelFree Reinforcement Learning
Withdrawn from Conference on Robot Learning (CORL), 2017
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 outofclass (e.g., linear model for nonlinear 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
Understand and Overcome the Limitations of MBRL
 Are accurate models condition necessary for good control performance?
 Are accurate models condition sufficient for good control performance?
(NO)
Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
GoalDriven Dynamics Learning via Bayesian Optimization
IEEE Conference on Decision and Control (CDC), 2017, 51685173
All models are wrong, but some are useful
 George E.P. Box
Very wrong models, can be very useful
 Roberto Calandra
If wrong models can be useful,
Can correct models be ineffective?
Lambert, N.; Amos, B.; Yadan, O. & Calandra, R.
Objective Mismatch in Modelbased Reinforcement Learning
Learning for DynamIcs & Control (L4DC), 2020
Objective Mismatch
Objective mismatch arises when one objective is optimized in the hope that a second, often uncorrelated, metric will also be optimized.
Negative LogLikelihood
Task Reward
Model Likelihood vs Episode Reward
Likelihood vs Reward
Deterministic model
Probabilistic model
Where is this assumption coming from?
Historical assumption ported from System Identification
Assumption: Optimizing the likelihood will optimize the reward
System Identification
Modelbased 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]
 endtoend differentiable models [Amos et al. 2019]
 ...
 Move away from the singletask formulation to multitask
 ???
Reweighted Likelihood
How can we give more importance to data that are important for the specific task at hand?
Our attempt: reweight data w.r.t. distance from optimal trajectory
Reweighted Likelihood
Understand and Overcome the Limitations of MBRL
 Are accurate models condition necessary for good control performance?
 Are accurate models condition sufficient for good control performance?
 Can we avoid the multiplicative error of recursive onestep predictions?
Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
GoalDriven Dynamics Learning via Bayesian Optimization
IEEE Conference on Decision and Control (CDC), 2017, 51685173
(NO)
(NO)
Lambert, N.; Amos, B.; Yadan, O. & Calandra, R.
Objective Mismatch in Modelbased Reinforcement Learning
Learning for Dynamics and Control (L4DC), 2020, 761770
1Step Ahead Models and their Propagation
Multiplicative Error  Doomed to accumulate
Trajectory Prediction
Lambert, N.; Wilcox, A.; Zhang, H.; Pister, K. S. J. & Calandra, R.
Learning Accurate Longterm Dynamics for Modelbased Reinforcement Learning
Under review, 2020, [available online: https://arxiv.org/abs/2012.09156]
Trajectory Prediction
Results
Lambert, N.; Wilcox, A.; Zhang, H.; Pister, K. S. J. & Calandra, R.
Learning Accurate Longterm Dynamics for Modelbased Reinforcement Learning
Under review, 2020, [available online: https://arxiv.org/abs/2012.09156]
Advantages
 Better accuracy for long horizons
 Calibrated uncertainty over the whole trajectory
 Better data efficiency
 Faster computation/propagation for longhorizons
(from O(t) to O(1) for any given t)
Understand and Overcome the Limitations of MBRL
 Can we avoid the multiplicative error of recursive onestep predictions?
Lambert, N.; Wilcox, A.; Zhang, H.; Pister, K. S. J. & Calandra, R.
Learning Accurate Longterm Dynamics for Modelbased Reinforcement Learning
Under review, 2020, [available online: https://arxiv.org/abs/2012.09156]
(YES)
 Can we dynamically tune the hyperparameters?
 Are accurate models condition necessary for good control performance?
 Are accurate models condition sufficient for good control performance?
Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
GoalDriven Dynamics Learning via Bayesian Optimization
IEEE Conference on Decision and Control (CDC), 2017, 51685173
(NO)
(NO)
Lambert, N.; Amos, B.; Yadan, O. & Calandra, R.
Objective Mismatch in Modelbased Reinforcement Learning
Learning for Dynamics and Control (L4DC), 2020, 761770
Hyperparameters are crucial for MBRL
 MBRL has many hyperparameters that need to be tuned
 Usually manually tuned
 Can we automatize the search for good hyperparameters using AutoML?
 Even more, can we go beyond static hyperparameters?
Example
Zhang, B.; Rajan, R.; Pineda, L.; Lambert, N.; Biedenkapp, A.; Chua, K.; Hutter, F. & Calandra, R.
On the Importance of Hyperparameter Optimization for Modelbased Reinforcement Learning
International Conference on Artificial Intelligence and Statistics (AISTATS), 2021
Results
Zhang, B.; Rajan, R.; Pineda, L.; Lambert, N.; Biedenkapp, A.; Chua, K.; Hutter, F. & Calandra, R.
On the Importance of Hyperparameter Optimization for Modelbased Reinforcement Learning
International Conference on Artificial Intelligence and Statistics (AISTATS), 2021
Results
Zhang, B.; Rajan, R.; Pineda, L.; Lambert, N.; Biedenkapp, A.; Chua, K.; Hutter, F. & Calandra, R.
On the Importance of Hyperparameter Optimization for Modelbased Reinforcement Learning
International Conference on Artificial Intelligence and Statistics (AISTATS), 2021
Conclusion
 Automatically tuning the hyperparameters of MBRL is a really good idea
 Dynamically tuning them is even better
 And conceptually a very interesting thing to do
(Rejection mechanism for data?)
Understand and Overcome the Limitations of MBRL
 Can we avoid the multiplicative error of recursive onestep predictions?
Lambert, N.; Wilcox, A.; Zhang, H.; Pister, K. S. J. & Calandra, R.
Learning Accurate Longterm Dynamics for Modelbased Reinforcement Learning
Under review, 2020, [available online: https://arxiv.org/abs/2012.09156]
(YES)
 Can we dynamically tune the hyperparameters?
Zhang, B.; Rajan, R.; Pineda, L.; Lambert, N.; Biedenkapp, A.; Chua, K.; Hutter, F. & Calandra, R.
On the Importance of Hyperparameter Optimization for Modelbased Reinforcement Learning
International Conference on Artificial Intelligence and Statistics (AISTATS), 2021
(YES)
 Are accurate models condition necessary for good control performance?
 Are accurate models condition sufficient for good control performance?
Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
GoalDriven Dynamics Learning via Bayesian Optimization
IEEE Conference on Decision and Control (CDC), 2017, 51685173
(NO)
(NO)
Lambert, N.; Amos, B.; Yadan, O. & Calandra, R.
Objective Mismatch in Modelbased Reinforcement Learning
Learning for Dynamics and Control (L4DC), 2020, 761770
A Few Applications
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 ModelBased Reinforcement Learning
IEEE Robotics and Automation Letters (RAL), 2019, 4, 42244230
MBRL on Physical Systems
Belkhale, S.; Li, R.; Kahn, G.; McAllister, R.; Calandra, R. & Levine, S.
ModelBased MetaReinforcement Learning for Flight with Suspended Payloads
IEEE Robotics and Automation Letters (RAL), 2021, 6, 14711478
Lambeta, M.; Chou, P.W.; Tian, S.; Yang, B.; Maloon, B.; Most, V. R.; Stroud, D.; Santos, R.; Byagowi, A.; Kammerer, G.; Jayaraman, D. & Calandra, R.
DIGIT: A Novel Design for a LowCost Compact HighResolution Tactile Sensor with Application to InHand Manipulation
IEEE Robotics and Automation Letters (RAL), 2020, 5, 38383845
Fine Manipulation using Touch
MBRL in Raw Tactile Space
Lambeta, M.; Chou, P.W.; Tian, S.; Yang, B.; Maloon, B.; Most, V. R.; Stroud, D.; Santos, R.; Byagowi, A.; Kammerer, G.; Jayaraman, D. & Calandra, R.
DIGIT: A Novel Design for a LowCost Compact HighResolution Tactile Sensor with Application to InHand Manipulation
IEEE Robotics and Automation Letters (RAL), 2020, 5, 38383845
Marble Manipulation
Lambeta, M.; Chou, P.W.; Tian, S.; Yang, B.; Maloon, B.; Most, V. R.; Stroud, D.; Santos, R.; Byagowi, A.; Kammerer, G.; Jayaraman, D. & Calandra, R.
DIGIT: A Novel Design for a LowCost Compact HighResolution Tactile Sensor with Application to InHand Manipulation
IEEE Robotics and Automation Letters (RAL), 2020, 5, 38383845
Future Directions
 Better Models
 Better Planning
 Deploying MBRL in the real world can still be daunting
 MBRL from Images
 Beyond 1step ahead models, towards Hierarchical Planning
A PyTorch Library for MBRL
Pineda, L.; Amos, B.; Zhang, A.; Lambert, N. O. & Calandra, R.
MBRLLib: A Modular Library for Modelbased Reinforcement Learning
Arxiv, 2021 https://arxiv.org/abs/2104.10159
 Implementing and debugging MBRL algorithms is notoriously difficult
 MBRLLib is the first PyTorch library dedicated to MBRL
 Two Goals:
 Highquality, easytouse baselines
 Framework for quickly implementing and validate new algorithms
 Plan to grow and support this library in the longterm
 Contributions are welcome!
Human Collaborators
Conclusion

Modelbased RL is a compelling framework for efficiently learn motor skills
 Orders of magnitude more dataefficient compared to modelfree approaches
 The decisionmaking process can be analyzed and explained

Discussed several theoretical and empirical limitations of current approaches
 Many aspects are still poorly understood:
 What and how to best model the relevant aspects of the world?
 How to efficiently use these models?
 Our goal is to better understand and improve existing algorithms to make them easier to use and more effective.

MBRLLib is a new opensource library dedicated to MBRL:
https://github.com/facebookresearch/mbrllib 
If you are interested in MBRL, I would be delighted to collaborate.
Thank you!
PS: This course is amazing! Wish I had this course 10 years ago...
Backup Slides
References
 Deisenroth, M.; Fox, D. & Rasmussen, C.
Gaussian Processes for DataEfficient Learning in Robotics and Control
IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 2014, 37, 408423  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, 47544765  Tian, S.; Ebert, F.; Jayaraman, D.; Mudigonda, M.; Finn, C.; Calandra, R. & Levine, S.
Manipulation by Feel: TouchBased 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 ModelBased Reinforcement Learning
IEEE Robotics and Automation Letters (RAL), 2019, 4, 42244230 
Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
GoalDriven Dynamics Learning via Bayesian Optimization
IEEE Conference on Decision and Control (CDC), 2017, 51685173 
Lambert, N.; Amos, B.; Yadan, O. & Calandra, R.
Objective Mismatch in Modelbased Reinforcement Learning
Under review, Soon on Arxiv, 2019
Ablation Study
Fast and Explainable Adaptation through Model Learning
 Modelbased learning algorithms
 Orders of magnitude more dataefficient compared to modelfree approaches
 The decisionmaking process can be analyzed and explained
 Many aspects are still poorly understood:
 what and how to best model the relevant aspects of the world?
 how to efficiently use these models?
 Our goal is to better understand and improve existing algorithms to make them easier to use and more effective.
References (of our work on modelbased RL)
 Belkhale, S.; Li, R.; Kahn, G.; McAllister, R.; Calandra, R. & Levine, S.
ModelBased MetaReinforcement Learning for Flight with Suspended Payloads
Under review, 2020  Lambert, N.; Wilcox, A.; Zhang, H.; Pister, K. S. J. & Calandra, R.
Learning Accurate Longterm Dynamics for Modelbased Reinforcement Learning
Under review, 2020  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, 47544765  Lambert, N. O.; Drew, D. S.; Yaconelli, J.; Levine, S.; Calandra, R. & Pister, K. S. J.
Low Level Control of a Quadrotor with Deep ModelBased Reinforcement Learning
IEEE Robotics and Automation Letters (RAL), 2019, 4, 42244230  Lambert, N.; Amos, B.; Yadan, O. & Calandra, R.
Objective Mismatch in Modelbased Reinforcement Learning
Learning for Dynamics and Control (L4DC), 2020, 761770  Bansal, S.; Calandra, R.; Xiao, T.; Levine, S. & Tomlin, C. J.
GoalDriven Dynamics Learning via Bayesian Optimization
IEEE Conference on Decision and Control (CDC), 2017, 51685173  Tian, S.; Ebert, F.; Jayaraman, D.; Mudigonda, M.; Finn, C.; Calandra, R. & Levine, S.
Manipulation by Feel: TouchBased Control with Deep Predictive Models
IEEE International Conference on Robotics and Automation (ICRA), 2019, 818824  Lambeta, M.; Chou, P.W.; Tian, S.; Yang, B.; Maloon, B.; Most, V. R.; Stroud, D.; Santos, R.; Byagowi, A.; Kammerer, G.; Jayaraman, D. & Calandra, R.
DIGIT: A Novel Design for a LowCost Compact HighResolution Tactile Sensor with Application to InHand Manipulation
IEEE Robotics and Automation Letters (RAL), 2020, 5, 38383845
References
 Yuan, W.; Dong, S. & Adelson, E. H.
GelSight: HighResolution Robot Tactile Sensors for Estimating Geometry and Force
Sensors, 2017  Calandra, R.; Owens, A.; Jayaraman, D.; Yuan, W.; Lin, J.; Malik, J.; Adelson, E. H. & Levine, S.
More Than a Feeling: Learning to Grasp and Regrasp using Vision and Touch
IEEE Robotics and Automation Letters (RAL), 2018, 3, 33003307  Allen, P. K.; Miller, A. T.; Oh, P. Y. & Leibowitz, B. S.
Integration of vision, force and tactile sensing for grasping
Int. J. Intelligent Machines, 1999, 4, 129149  Chebotar, Y.; Hausman, K.; Su, Z.; Sukhatme, G. S. & Schaal, S.
Selfsupervised regrasping using spatiotemporal tactile features and reinforcement learning
International Conference on Intelligent Robots and Systems (IROS), 2016  Schill, J.; Laaksonen, J.; Przybylski, M.; Kyrki, V.; Asfour, T. & Dillmann, R.
Learning continuous grasp stability for a humanoid robot hand based on tactile sensing
BioRob, 2012  Bekiroglu, Y.; Laaksonen, J.; Jorgensen, J. A.; Kyrki, V. & Kragic, D.
Assessing grasp stability based on learning and haptic data
Transactions on Robotics, 2011, 27  Sommer, N. & Billard, A.
Multicontact haptic exploration and grasping with tactile sensors
Robotics and autonomous systems, 2016, 85, 4861
Theory and Practice of Modelbased Reinforcement Learning [Caltech]
By Roberto Calandra
Theory and Practice of Modelbased Reinforcement Learning [Caltech]
 1,289