Source-linked AI summary
Maximum Entropy Deep Inverse Reinforcement Learning
Markus Wulfmeier, Peter Ondruska, Ingmar Posner
TL;DR
IRL seeks to infer reward structures guiding behavior, but existing representations and kernel methods can be limited for complex rewards and large-scale data. The paper introduces Maximum Entropy Deep IRL with neural reward approximation and evaluates it against prior methods. DeepIRL matches state-of-the-art performance on a common benchmark, outperforms it on a more complex benchmark, and can learn spatial features from raw inputs.
Problem
IRL requires inferring complex reward structures from observed behavior, while feature-based representations and kernel methods face limits in nonlinear expressiveness or scalability.
Method
DeepIRL combines neural-network reward approximation with Maximum Entropy IRL, using fully differentiable training and convolutional architectures for spatial feature learning.
Results
DeepIRL matches state-of-the-art performance on a common benchmark and significantly outperforms it on a new benchmark with more complex reward structure.
Takeaways & Limitations
The approach provides demonstration-independent query complexity and supports life-long learning scenarios while extending reward learning to raw regularly gridded inputs.
Takeaways & Limitations
DeepIRL requires additional training data to maintain equal accuracy as network parameters increase, and automatically learned features cannot exceed optimal predefined features in simplified benchmarks.
Abstract
from arXiv · showhide
This paper presents a general framework for exploiting the representational capacity of neural networks to approximate complex, nonlinear reward functions in the context of solving the inverse reinforcement learning (IRL) problem. We show in this context that the Maximum Entropy paradigm for IRL lends itself naturally to the efficient training of deep architectures. At test time, the approach leads to a computational complexity independent of the number of demonstrations, which makes it especially well-suited for applications in life-long learning scenarios. Our approach achieves performance commensurate to the state-of-the-art on existing benchmarks while exceeding on an alternative benchmark based on highly varying reward structures. Finally, we extend the basic architecture - which is equivalent to a simplified subclass of Fully Convolutional Neural Networks (FCNNs) with width one - to include larger convolutions in order to eliminate dependency on precomputed spatial features and work on raw input representations.
1. Introduction
The introduction motivates IRL as learning reward structures from demonstrations and presents neural, Maximum Entropy, and convolutional architectures for scalable nonlinear reward approximation.
- IRL infers the reward structure guiding an agent’s behaviour from observations and an environment model.
- Prior IRL methods commonly use predetermined features, including weighted linear combinations, which can limit nonlinear reward representation.
- Kernel-based nonlinear approaches can scale poorly because query complexity depends on training data or active inducing points, especially for highly varying rewards.
- Neural networks approximate complex nonlinear rewards compactly and provide O(1) query complexity with respect to observed demonstrations.
- Fully Convolutional Neural Networks can use wider convolutions to analyze states with spatial context instead of relying only on individual feature representations.
- Maximum Entropy IRL yields an objective that is fully differentiable with respect to deep-network weights without approximations.
2. Inverse Reinforcement Learning
Inverse reinforcement learning infers an unknown reward structure from expert demonstrations in a known environment. Maximum Entropy IRL models distributions over trajectories, while reward-function approximation addresses large state spaces and nonlinear rewards.
- Inverse Reinforcement Learning: IRL infers the hidden reward structure from expert state-action demonstrations when the MDP specification is available but rewards are unknown.The inferred reward can support modelling or imitation of a demonstrator’s behaviour.
- Maximum Entropy IRL: Maximum Entropy IRL assigns trajectory preferences in proportion to the exponential of the reward along each path.This formulation operates over trajectory distributions rather than requiring perfectly optimal demonstrations.
- Reward Function Approximation: Feature-based reward approximation constrains states with similar features to have similar real-valued rewards, supporting generalisation and transfer across scenarios sharing representations.Feature representations may be hand-crafted or learned within the proposed framework.
- Nonlinear Reward Models: Linear reward models are limited when the true reward is not accurately approximated by a linear function.Composite logical features remain limited to piecewise constant functions, despite extending the linear model.
- Gaussian-Process IRL: GPIRL can model complex nonlinear rewards, but its computational complexity grows with demonstrations and active inducing points, which depend on reward complexity.The active set can become unwieldy for large state spaces and complex rewards.
3. Reward Function Approximation with Deep Architectures
Deep architectures are proposed for representing complex nonlinear reward structures in large-feature-space IRL. Maximum Entropy training remains differentiable through the reward network, enabling backpropagation and task-specific architectures.
- Deep Architectures: Deep architectures represent complex nonlinear rewards by reusing computations across layers while balancing network depth and breadth.The paper motivates them for IRL problems with large feature spaces.
- Network Architecture: The proposed network maps state features to state rewards through learned network parameters.This architecture provides the reward-function approximation used by DeepIRL.
- Architecture Choices: Convolutional layers can adapt the network to individual tasks and remove dependence on hand-crafted spatial features.The framework supports a broad range of architecture choices, including FCNNs.
- Fully Convolutional Networks: FCNN padding produces reward maps with the same spatial dimensionality as the input, while deconvolutions provide another way to reshape outputs accordingly.The output retains spatial correspondence with the input representation.
- Training Procedure: Maximum Entropy IRL provides an objective that is fully differentiable with respect to neural-network weights without approximations.The resulting gradients can be optimized with standard methods such as conjugate gradient or stochastic gradient descent.
- Gradient Computation: DeepIRL separates the loss derivative with respect to rewards from the derivative of rewards with respect to network weights, applying backpropagation for the latter.The complete gradient includes the data-term gradient and a weight-decay regulariser.
Input: µa
The DeepIRL procedure iteratively solves the MDP under the current reward, computes Maximum Entropy losses and gradients, and propagates visitation-based error signals through the network. FCNN training evaluates all state-wise rewards together using receptive fields.
- Gradient Computation: Dynamic programming computes expected visitation quantities in polynomial time instead of summing over exponentially many trajectories.The resulting visitation-count difference is passed through the network by backpropagation.
- Maximum Entropy Deep IRL: Algorithm 1 trains Maximum Entropy Deep IRL by iteratively refining the reward model using loss and gradient calculations.The procedure uses expert state-action frequencies in its loss computation.
- Approximate Value Iteration: Approximate Value Iteration determines the policy under the current reward through iterative updates of the state-action value function.This is the MDP-solving stage of the main algorithm.
- Policy Propagation: Policy Propagation computes expected state-visitation frequencies by probabilistically traversing the MDP.These visitation frequencies contribute to the Maximum Entropy gradient.
- FCNN Training: FCNN training sums losses over all states at once, making receptive fields functionally equivalent to a minibatch and more efficient than separate field computations.Each output reward is influenced by its corresponding receptive field in the original state space.
4. Experiments
The experiments compare DeepIRL with established IRL methods on Objectworld and Binaryworld, including training, transfer, feature, and raw spatial representations. DeepIRL matches GPIRL as demonstrations increase and better captures highly varying higher-order reward structures, with additional data needed when learning features from raw inputs.
- Experimental setup: The experiments compare DeepIRL with GPIRL, NPB-FIRL, and original MaxEnt across two benchmark tasks and training and transfer scenarios.Demonstrations are synthetically generated from optimal policies with 30% random actions, and expected value difference measures learned-policy suboptimality under the true reward.
- Objectworld Benchmark: Objectworld rewards depend on specific distances to two colors, with positive reward near both, negative reward near only color 1, and zero otherwise.The benchmark uses continuous and discrete state-feature representations and includes randomly generated transfer scenarios to test overfitting.
- Objectworld Benchmark: DeepIRL and GPIRL significantly outperform original MaxEnt on Objectworld’s nonlinear reward structure.GPIRL performs well with few demonstrations, while DeepIRL reaches commensurate performance as the number of expert demonstrations increases, under both feature representations.
- Binaryworld Benchmark: Both DeepIRL and GPIRL are robust to distractor variables, although DeepIRL shows minimally greater overfitting as distractors increase.The paper attributes this to neural-network capacity being applied to noise and proposes additional regularization as future work.
- Binaryworld Benchmark: Binaryworld requires learning higher-order relationships among nine local binary features, because reward depends on whether exactly four or five neighboring states are blue.This makes the benchmark more complex than Objectworld, where individual feature values carry more direct information.
- Binaryworld Benchmark: DeepIRL learns Binaryworld’s higher-order dependencies, while GPIRL needs more demonstrations and NPB-FIRL cannot efficiently represent the reward with its logical conjunctions.Accurate NPB-FIRL representation would require 29 different conjunctions covering all possible feature combinations.
- Spatial Feature Learning: Learning spatial features from raw inputs converges toward performance with predefined features, but equal accuracy requires additional training data as network parameters increase.The toy benchmarks use optimal predefined features, while raw-data feature learning is motivated by information loss during real-world compression.
5. Conclusion and Future Work
DeepIRL uses FCNNs to approximate reward structures in IRL, supporting complex rewards in large state spaces and adaptable architectures. Its evaluation matches state of the art on a common benchmark, outperforms it on a more complex benchmark, and extends to raw inputs; future work targets wider-filter training demands.
- Conclusion: DeepIRL exploits FCNNs to approximate reward structures for complex tasks and large state spaces.The framework also supports custom network architectures using the same training cost function.
- Conclusion: DeepIRL matches state-of-the-art performance on a common benchmark and significantly outperforms current methods on a benchmark with more complex reward structures.The alternative benchmark evaluates the model’s ability to represent interactions between features.
- Conclusion: Wider convolutional filters remove dependence on precomputed features and extend DeepIRL toward raw input representations.This extension emphasizes the adaptability of framing IRL within deep learning.
- Future Work: Future work will investigate autoencoder-style pretraining to reduce the increased demand for expert demonstrations when using wider convolutional filters.The proposed direction is especially relevant for complex inputs such as raw image data, where unsupervised data can support feature learning.