Source-linked AI summary
Adversarial Imitation via Variational Inverse Reinforcement Learning
Ahmed H. Qureshi, Byron Boots, Michael C. Yip
TL;DR
Learning rewards and policies from expert examples under unknown dynamics is challenging, particularly when demonstrations leave reward functions ambiguous. The paper introduces EAIRL, which learns empowerment alongside rewards and policies using variational information maximization and empowerment-regularized adversarial IRL. It reports near-optimal, expert-matching rewards and policies and stronger IRL performance, while assuming training demonstrations come from a single expert.
Problem
Learning rewards from expert demonstrations is challenging because many optimal policies can explain the demonstrations and many reward functions can induce an optimal policy.
Source: §1 · p. 2Method
Results
Takeaways & Limitations
The learned state-action rewards are described as robust and transferable, with evaluation including environments that differ in dynamics or structure.
Source: §1 · p. 2, §5 · p. 9The method assumes a single expert generates the training data; learning from diverse demonstrations remains future work.
Source: §6 · p. 9
Abstract
from arXiv · showhide
We consider a problem of learning the reward and policy from expert examples under unknown dynamics. Our proposed method builds on the framework of generative adversarial networks and introduces the empowerment-regularized maximum-entropy inverse reinforcement learning to learn near-optimal rewards and policies. Empowerment-based regularization prevents the policy from overfitting to expert demonstrations, which advantageously leads to more generalized behaviors that result in learning near-optimal rewards. Our method simultaneously learns empowerment through variational information maximization along with the reward and policy under the adversarial learning formulation. We evaluate our approach on various high-dimensional complex control tasks. We also test our learned rewards in challenging transfer learning problems where training and testing environments are made to be different from each other in terms of dynamics or structure. The results show that our proposed method not only learns near-optimal rewards and policies that are matching expert behavior but also performs significantly better than state-of-the-art inverse reinforcement learning algorithms.
1 INTRODUCTION
The introduction motivates learning rewards from demonstrations because reward design is difficult and direct imitation does not recover portable rewards. It presents EAIRL as an empowerment-regularized adversarial IRL method that learns rewards and policies from expert data.
1 INTRODUCTION
- Reward design is challenging in robotic applications such as social interaction, dexterous manipulation, and autonomous driving.These tasks require desired behavior to be encoded in an optimizable reward function.Source: §1 · p. 1
- Maximum-entropy IRL can use neural function approximators under unknown dynamics, but IRL design may require hand-engineered, domain-specific regularizers.The introduction identifies this engineering burden as a challenge for IRL algorithms.Source: §1 · p. 1
- Behavior cloning learns policies by supervised learning from expert trajectories, but covariate shift can cause compounding errors and require substantial data.GAIL uses a generator-discriminator framework to train policies to produce expert-like trajectories, but does not recover transferable rewards.Source: §1 · pp. 1–2
- Reward learning is ambiguous because many optimal policies can explain demonstrations and many reward functions can induce an optimal policy.AIRL addresses the former issue through maximum-entropy IRL, but its state-only reward cannot recover ground-truth rewards that depend on actions.Source: §1 · p. 2
- EAIRL learns near-optimal rewards and policies, with reward-learning results outperforming several state-of-the-art IRL methods and policy results outperforming AIRL with state-only rewards and GAN-GCL.Its policies perform comparably to GAIL and AIRL using non-disentangled state-action rewards.Source: §1 · p. 2
2 BACKGROUND
The background sets out the MDP and trajectory-distribution foundations, then reviews adversarial IRL and empowerment as a mutual-information-based potential. It describes variational information maximization as a scalable route to learning empowerment.
2 BACKGROUND
- An MDP specifies state and action spaces, transition and reward functions, an initial-state distribution, and a discount factor.The paper also defines policies, trajectories, an inverse model, and a potential function within this framework.Source: §2 · p. 2
2.1 MAXENT-IRL
- Maximum-entropy IRL models expert trajectories with a Boltzmann distribution whose energy is the parameterized trajectory reward, and estimates its partition function under unknown dynamics by importance sampling.Demonstrations are treated as samples from an optimal policy, while less rewarding trajectories receive exponentially decaying probability.Source: §2.1 · p. 3
2.2 ADVERSARIAL INVERSE REINFORCEMENT LEARNING
- AIRL extends GAIL to recover rewards alongside policies by training a discriminator with a disentangled state-only reward and a potential-based shaping term.Its shaping function has free parameters and is tied to the recovered reward up to a constant, limiting the benefits of reward shaping.Source: §2.2 · p. 3
2.3 EMPOWERMENT AS MAXIMAL MUTUAL INFORMATION
- Empowerment measures how actions influence future states; a variational lower bound makes mutual-information maximization scalable beyond the small problems previously feasible.The method optimizes a policy and scalar potential to match the policy-plus-potential approximation to an inverse-model action likelihood, with an entropy constraint to prevent divergence.Source: §2.3 · p. 4
3 EMPOWERED ADVERSARIAL INVERSE REINFORCEMENT LEARNING
EAIRL jointly learns an inverse model, reward, empowerment-based potential, and policy from expert demonstrations. Its policy objective combines the discriminator reward with empowerment regularization.
3 EMPOWERED ADVERSARIAL INVERSE REINFORCEMENT LEARNING
- EAIRL jointly trains an inverse model, state-action reward, empowerment-based potential, and policy to recover optimal policies and generalizable rewards.The potential shapes the reward and regularizes policy updates; the method considers immediate-step transitions (K = 1).Source: §3 · pp. 4–5
3.1 INVERSE MODEL qφ(a|s, s′) OPTIMIZATION
- The inverse model minimizes mean-square error between its predicted action and the action taken in policy-generated trajectories.It maps the current and next states to a distribution over actions.Source: §3.1 · p. 5
3.2 EMPOWERMENT Φϕ(s) OPTIMIZATION
- Empowerment is approximated through the normalization function Z(s) of optimal w*(a|s), with its estimate trained by minimizing lI on policy-generated transitions.The loss is optimized with respect to potential parameters ϕ.Source: §3.2 · p. 5
3.3 REWARD FUNCTION rξ(s, a)
- The discriminator distinguishes expert from generated trajectories, while a periodically updated target potential is maintained to stabilize learning.The target parameters ϕ′ are updated from ϕ every n training epochs.Source: §3.3 · p. 5
3.4 POLICY OPTIMIZATION POLICY πθ(a|s)
- Policy updates maximize the discriminative reward while minimizing the empowerment loss, equivalent to the MaxEnt-IRL policy objective with added empowerment maximization.The policy is regularized by empowerment to induce generalized behavior rather than locally overfit limited demonstrations.Source: §3.4 · pp. 5–6
4 RESULTS
The experiments evaluate reward and policy learning on control tasks, including transfer to changed testing environments. EAIRL’s learned rewards nearly match expert performance after transfer, while its imitation policies perform similarly to several state-action or adversarial methods.
4 RESULTS
- The experiments compare EAIRL with policy- and reward-learning methods using mean and standard deviation of accumulated rewards across five randomly seeded trials.The policy-learning comparisons include GAIL, GAN-GCL, AIRL(s), and AIRL(s, a); reward-learning comparisons include AIRL(s) and AIRL(s, a).Source: §4 · pp. 6–7
4.1 REWARD LEARNING PERFORMANCE (TRANSFER LEARNING EXPERIMENTS)
- EAIRL’s transfer scores nearly reach expert scores in all five trials and significantly outperform AIRL(s) and AIRL(s, a).The evaluation reports mean scores and standard deviations over five trials.Source: Figure 2 · p. 7, §4.1 · pp. 7–8, Table 1 · p. 7
4.2 POLICY LEARNING PERFORMANCE (IMITATION LEARNING)
- EAIRL, AIRL(s, a), and GAIL show similar imitation performance, while AIRL(s) and GAN-GCL fail to recover a policy.The evaluation covers halfcheetah, ant, swimmer, and pendulum control tasks.Source: §4.2 · p. 8, Table 2 · p. 8
5 DISCUSSION
The discussion links empowerment regularization to broader policy behavior and argues that reward and discriminator functions need state-action inputs. It connects that formulation to recovering action-dependent reward terms and expert-like policies.
5 DISCUSSION
- Empowerment regularization balances reducing divergence from expert data with maximizing control over the environment, preventing premature convergence to localized behavior.The authors link this to robust state-action reward learning.Source: §5 · p. 8
- State-only AIRL rewards miss action-dependent high-torque penalties, producing aggressive behavior that can make the crippled ant reach only halfway to expert scores.The authors report that the agent sometimes flips over after a few steps.Source: §5 · p. 9
- State-action reward or discriminator formulations are reported to recover expert-like policies, whereas adversarial imitation can fail to learn ground-truth rewards and expert-like policies without them.The discussion treats action-dependent costs as relevant to driving, locomotion, and manipulation tasks.Source: §5 · pp. 8–9
6 CONCLUSIONS AND FUTURE WORK
The conclusion presents empowerment-regularized maximum-entropy IRL as a way to learn rewards and policies from expert demonstrations. The authors identify single-expert training as an assumption and propose diverse or sub-optimal demonstrations as future directions.
6 CONCLUSIONS AND FUTURE WORK
- EAIRL learns empowerment through variational information maximization alongside reward and policy, with regularization intended to prevent premature local convergence and support generalized policies.The authors report near-optimal rewards and policies and transfer to environments with changed dynamics or structure.Source: §6 · p. 9
- The method assumes training data come from a single expert; learning from diverse experts and sub-optimal demonstrations remains future work.The proposed extension would include demonstrations containing both optimal and non-optimal behavior.Source: §6 · p. 9
APPENDICES
The appendix presents a variational lower-bound derivation for learning empowerment.
APPENDICES
- The appendix derives mutual information as a variational lower bound and uses its maximization to learn empowerment.Source: A VARIATIONAL EMPOWERMENT · p. 11
A.1 VARIATIONAL INFORMATION LOWER BOUND
The appendix derives a variational lower bound for empowerment and incorporates it into maximum-entropy inverse reinforcement learning. The resulting policy objective combines learned reward, empowerment, and regularization terms.
A.1 VARIATIONAL INFORMATION LOWER BOUND
- The mutual-information lower bound is expressed using conditional entropy, an inverse-model log-likelihood term, and a KL term.The appendix describes mutual information as a difference in conditional entropies and presents the variational lower-bound derivation.Source: §A.1 · p. 11, §A.2 · p. 11
A.2 VARIATIONAL INFORMATION MAXIMIZATION
- Optimizing the inverse model is a supervised maximum-likelihood problem, while the variational action distribution has a softmax form based on expected log inverse-model probability.For discrete state and action spaces, the stated solution is proportional to exp(u(s, a)), where u uses the expected log q(a|s′, s).Source: §A.2 · p. 11
B EMPOWERMENT-REGULARIZED MAXENT-IRL FORMULATION.
- The policy is trained to maximize empowerment while reducing its trajectory-distribution divergence from the reward-induced distribution, yielding an entropy-regularized update.The derivation notes that matching trajectory terms cancel in the divergence objective.Source: B EMPOWERMENT-REGULARIZED MAXENT-IRL… · p. 12
B.1 POLICY OBJECTIVE
- The policy reward combines learned reward with an empowerment potential and entropy and inverse-model terms.The text gives the form rπ(s, a, s′) = r(s, a, s′) + γΦ(s′) + (λI − λh) log π(a|s) − λI log q(a|s, s′).Source: §B.1 · pp. 12–13
C.1 ANT ENVIRONMENT
The transfer examples show distinct adaptations to changed conditions: a crippled ant changes its gait, and a point-mass agent takes a different route in the test maze.
C.1 ANT ENVIRONMENT
- The standard ant can move sideways, whereas the crippled ant must rotate to move forward.Figure 4’s top and bottom rows show the standard and crippled ant gaits, respectively.Source: §C.1 · p. 13, Figure 4 · p. 13
- Figure 4’s top and bottom rows show the gaits of the standard and crippled ants, respectively.The accompanying description distinguishes their path profiles and movement capabilities.Source: Figure 4 · p. 13, §C.1 · p. 13
C.2 MAZE ENVIRONMENT
- In the testing maze, the point-mass agent takes the opposite route from its training-environment route to reach the target.Source: §C.2 · p. 13
D.1 NETWORK ARCHITECTURES
The experiments use compact two-layer ReLU networks for the models and specify separate regularization settings for reward and policy learning.
D.1 NETWORK ARCHITECTURES
- The potential, reward, discriminator, policy, and inverse-model networks use two layers with 32 units per layer.The policy and inverse-model outputs parameterize Gaussian distributions.Source: §D.1 · pp. 13–14
- Figure 5’s top and bottom rows show the point-mass agent’s path to the target in training and testing, respectively.Source: Figure 5 · p. 14
D.2 HYPERPARAMETERS
- Reward learning uses entropy weight 0.1 and information weight λI = 1.0, while policy learning uses 0.001 for both weights.The temperature is β = 1 for all experiments; target potential parameters are updated every 5 reward-learning epochs and every 2 policy-learning epochs.Source: §D.2 · p. 14