Using Inaccurate Models in Reinforcement Learning

Using Inaccurate Models

in Reinforcement Learning

Pieter Abbeel, Morgan Quigley and Andrew Y. Ng

Stanford University


Overview Reinforcement learning in high-dimensional

continuous state-spaces. Model-based RL: Difficult to build an accurate model. Model-free RL: Often requires large numbers of real-

life trials. We present a hybrid algorithm, which requires

only an approximate model, a small number of real-life trials.

Resulting policy is (locally) near-optimal. Experiments on flight simulator and real RC car.


Markov Decision Process (MDP) M = (S, A, T , H, s0, R ). S = n (continuous state space)

Time varying, deterministic dynamics T = { ft : S x A ! S, t = 0,…,H}.

Goal: find policy : S ! A, that maximizes U() = E [ R (st) | ].

Focus: task of trajectory following.

Reinforcement learning formalism

H

t=0


Motivating Example

Student-driver learning to make a 90 degree right turn Only a few trials needed. No accurate model.

Student-driver has access to: Real-life trial. Crude model.

Result: good policy gradient estimate.


Input to algorithm: approximate model. Start by computing the optimal policy

according to the model.

Algorithm Idea

Real-life trajectory

Target trajectory

The policy is optimal according to the model, so no improvement is possible based on the model.


Algorithm Idea (2)

Update the model such that it becomes exact for the current policy.


Algorithm Idea (2)

The updated model perfectly predicts the state sequence obtained under the current policy.

We can use the updated model to find an improved policy.


Algorithm

1. Find the (locally) optimal policy for the model.2. Execute the current policy and record the state

trajectory.3. Update the model such that the new model is exact

for the current policy .4. Use the new model to compute the policy gradient

and update the policy: := + 5. Go back to Step 2.

Notes: The step-size parameter is determined by a line search. Instead of the policy gradient, any algorithm that provides

a local policy improvement direction can be used. In our experiments we used differential dynamic programming.


Performance Guarantees: Intuition

Exact policy gradient:

Model based policy gradient:

Evaluation of derivatives along wrong trajectory

Derivative of approximate transition

function

Our algorithm eliminates one (of two) sources of error.


Performance Guarantees Let the local policy improvement algorithm be policy gradient.

Notes: These assumptions are insufficient to give the same

performance guarantees for model-based RL. The constant K depends only on the dimensionality of the

state, action, and policy (), the horizon H and an upper bound on the 1st and 2nd derivatives of the transition model, the policy and the reward function.


Experiments We use differential dynamic programming (DDP) to

find control policies in the model.

Two Systems: Flight Simulator RC Car


Flight Simulator Setup

Flight simulator model has 43 parameters (mass, inertia, drag coefficients, lift coefficients etc.).

We generated “approximate models” by randomly perturbing the parameters.

All 4 standard fixed-wing control actions: throttle, ailerons, elevators and rudder.

Our reward function quadratically penalizes for deviation from the desired trajectory.


Flight Simulator Movie


Flight Simulator Results

desired trajectorymodel-based controllerour algorithm

76% utility improvement over

model-based approach


RC Car Setup

Control actions: throttle and steering. Low-speed dynamics model with state variables:

Position, velocity, heading, heading rate. Model estimated from 30 minutes of data.


RC Car: Open-Loop Turn


RC Car: Circle


RC Car: Figure-8 Maneuver


Related Work Iterative Learning Control:

Uchiyama (1978), Longman et al. (1992), Moore (1993), Horowitz (1993), Bien et al. (1991), Owens et al. (1995), Chen et al. (1997), …

Successful robot control with limited number of trials: Atkeson and Schaal (1997), Morimoto and Doya

(2001). Robust control theory:

Zhou et al. (1995), Dullerud and Paganini (2000), … Bagnell et al. (2001), Morimoto and Atkeson (2002),

…


Conclusion We presented an algorithm that uses a crude

model and a small number of real-life trials to find a policy that works well in real-life.

Our theoretical results show that----assuming a deterministic setting and assuming a reasonable model----our algorithm returns a policy that is (locally) near-optimal.

Our experiments show that our algorithm can significantly improve on purely model-based RL by using only a small number of real-life trials, even when the true system is not deterministic.


Motivating Example

Student-driver learning to make a 90 degree right turn Only a few trials needed. No accurate model.

Key aspects Real-life trial: shows whether turn is wide or

short. Crude model: turning steering wheel more to the

right results in sharper turn, turning steering wheel more to the left results in wider turn.

Result: good policy gradient estimate.

Using Inaccurate Models in Reinforcement Learning

Documents

Transcript of Using Inaccurate Models in Reinforcement Learning