PaperlayerView exact revision on arXiv

Source-linked AI summary

Cooperative Inverse Reinforcement Learning

Dylan Hadfield-Menell, Anca Dragan, Pieter Abbeel, Stuart Russell

arXiv:1606.03137v4cs.AI

TL;DR

Value alignment requires autonomous systems to act on objectives that reflect human intent, a challenge made harder by humans’ tendency to misstate objectives. This paper formalizes the problem as cooperative inverse reinforcement learning and shows that optimal policy-pair computation can be reduced to a single-actor POMDP.

  • Problem

    Value alignment asks how autonomous systems can act on objectives that reflect human intent, given that humans may misstate their objectives.

    Source: §1 · p. 1

  • Method

    The paper models value alignment as cooperative inverse reinforcement learning, a cooperative game for human-reward maximization, and reduces optimal policy-pair computation to a POMDP.

    Source: §3.2 · p. 5, §5 · p. 8

  • Results

    CIRL’s optimal policy-pair problem is reducible to a single-actor POMDP with hidden state size |S| · |Θ|.

    Source: §3.2 · p. 5

  • Takeaways & Limitations

    CIRL provides a framework for designing HRI algorithms and analyzing both actors’ incentives in reward-learning settings.

    Source: §5 · p. 8

    The reduced POMDP can remain challenging because POMDPs are difficult and the reduced problem has a much larger action space.

    Source: §3.2 · p. 5

Abstract

from arXiv · show

For an autonomous system to be helpful to humans and to pose no unwarranted risks, it needs to align its values with those of the humans in its environment in such a way that its actions contribute to the maximization of value for the humans. We propose a formal definition of the value alignment problem as cooperative inverse reinforcement learning (CIRL). A CIRL problem is a cooperative, partial-information game with two agents, human and robot; both are rewarded according to the human's reward function, but the robot does not initially know what this is. In contrast to classical IRL, where the human is assumed to act optimally in isolation, optimal CIRL solutions produce behaviors such as active teaching, active learning, and communicative actions that are more effective in achieving value alignment. We show that computing optimal joint policies in CIRL games can be reduced to solving a POMDP, prove that optimality in isolation is suboptimal in CIRL, and derive an approximate CIRL algorithm.

1 Introduction

The paper frames value alignment as cooperative, interactive reward maximization: the robot receives the human’s reward but initially does not know its reward parameter. It argues that interaction can support instruction and learning, while expert behavior in isolation is not generally the best way to teach the robot.

Introduction

  • Ordinary IRL is insufficient for value alignment: the robot should optimize the human’s reward rather than adopt it, and assuming optimal behavior excludes useful teaching actions.The introduction illustrates how a mis-specified reward can produce unintended behavior and how demonstrations, explanations, questions, and guided practice can aid learning.Source: §1 · pp. 1–2

Cooperative inverse reinforcement learning

  • CIRL models value alignment as a cooperative partial-information game in which the robot’s payoff is the human’s reward, which the human knows and the robot must learn.Optimal solutions can involve active instruction by the human and active learning by the robot.Source: §1 · p. 2

Reduction to POMDP and Sufficient Statistics

  • CIRL policy optimization reduces to a single-agent POMDP, where the robot’s posterior over the reward parameter is a sufficient statistic for optimal behavior.The paper states this has exponentially lower complexity than the NEXP-hard bound for general Dec-POMDPs.Source: §1 · p. 2

Apprenticeship Learning and Suboptimality of IRL-Like Solutions

  • In apprenticeship learning, classic IRL is the robot’s best response to expert demonstrations, but that policy pair is generally suboptimal because other demonstrations can teach more effectively.The paper gives an approximate human best-response algorithm for linear rewards and state features, and reports that it outperforms expert demonstrations in an example game by teaching the value landscape.Source: §1 · p. 2

2 Related Work

The paper situates CIRL among inverse reinforcement learning, optimal teaching, and principal–agent models, distinguishing cooperative decision-making from fixed-policy inference, learner-directed teaching, and incentive design.

Inverse Reinforcement Learning

  • IRL’s demonstration-by-expert assumption treats observed behavior as reward-maximizing, but in CIRL H may accept less reward to teach R, making isolated optimality suboptimal.Under this assumption, CIRL prescribes a fixed policy for H.Source: §2 · p. 2
  • Prior IRL methods infer rewards for fixed human policies; in CIRL, their constraints characterize R’s belief under the demonstration-by-expert assumption.Ng & Russell (2000), Abbeel & Ng (2004), and Ratliff et al. (2006) use max-margin selection among consistent rewards; Ramachandran & Amir (2007) and Ziebart et al. (2008) model noisily expert policies.Source: §2 · p. 3

Optimal Teaching

  • CIRL differs from optimal teaching because efficient learning is its objective, whereas efficient teaching emerges as a property of CIRL equilibrium behavior.Cakmak & Lopes (2012) select initial states to reduce learner uncertainty; in CIRL, this is an approximate greedy entropy-minimizing strategy for H.Source: §2 · p. 3
  • CIRL’s approximate solution resembles methods that choose motion or speech to communicate intentions, goals, or groundings, but conveys the correct reward function.These approaches model observer inference and select actions to increase the probability of inferring the correct hypothesis or goal.Source: §2 · pp. 3–4

Principal–agent models

  • Unlike principal–agent models’ non-cooperative incentive design, CIRL’s AI alignment problem arises from information asymmetry because artificial agents lack intrinsic desires.Principal–agent models address misaligned incentives between people with their own desires.Source: §2 · p. 4

3 Cooperative Inverse Reinforcement Learning

CIRL models value alignment as a cooperative game in which human and robot share a reward function that only the human initially knows. The section reduces optimal policy computation to a POMDP and shows why apprenticeship demonstrations may need to teach rather than simply maximize immediate reward.

3.1 CIRL Formulation

  • CIRL is a two-player Markov game with identical payoffs, where the human observes the reward parameter θ and the robot initially does not.Sharing the reward function incentivizes the human to teach and the robot to learn without explicitly encoding those objectives.Source: §3.1 · p. 4

3.2 Structural Results for Computing Optimal Policy Pairs

  • Any CIRL policy pair can be represented by a POMDP policy with hidden-state size |S|·|Θ|; an optimal pair depends only on the current state and the robot’s belief.Because θ is the only private information, the reduction is exponentially smaller than a general Dec-POMDP, though the resulting POMDP may remain challenging and have a much larger action space.Source: §3.2 · p. 5

3.3 Apprenticeship Learning as a Subclass of CIRL Games

  • In ACIRL’s deployment phase, the robot’s optimal policy maximizes reward in the MDP induced by the mean θ in its belief.ACIRL consists of a turn-taking learning phase followed by a deployment phase in which the robot acts independently.Source: §3.3 · pp. 5–6
  • Under the demonstration-by-expert assumption, the human greedily maximizes immediate reward, but this need not be her best response when the robot responds optimally.In the example equilibrium, the human chooses (1, 1) for θ ∈ [41/92, 51/92], whereas the expert policy does so only at θ = 0.5; a short-term reward loss can improve the robot’s estimate.Source: §3.3 · p. 6

3.4 Generating Instructive Demonstrations

  • For linear rewards, instructive demonstrations trade off reward against similarity to expected feature counts, using an ℓ2 norm as a proxy for regret.The figure reports regret minimized at an intermediate λ: too little expected optimality yields little learning, while too much can make reward parameters indistinguishable from trajectories.Source: §3.4 · pp. 6–7, Figure 2 · p. 7

4 Experiments

In grid-navigation experiments, cooperative best-response demonstrations outperform expert demonstrations across all measured outcomes. Robot regret is lower when it assumes the human is noisily optimal at an intermediate level.

4.1 Cooperative Learning for Mobile Robot Navigation

  • The best-response policy visits both high-reward areas, producing a more representative inferred reward function than expert demonstrations.In the 2D grid task, the expert immediately goes to the highest reward and stays there; the robot observes a teleoperated learning trajectory before deployment.Source: §4.1 · p. 7

4.2 Demonstration-by-Expert vs Best Responder

  • Across policy regret, KL-divergence, and reward-vector ℓ2 norm, the br H-policy significantly outperformed πE on all measures (all F > 962, p < .0001).Source: §4.2 · p. 8

4.3 Varying R’s Expectations

  • Robot regret was lower at intermediate λ, where its model treats the human as noisily optimal rather than random or exactly optimal.At extreme λ values, many reward parameters map to the same expected feature counts or optimal trajectory, making them harder for the human to distinguish.Source: §4.3 · p. 8

5 Conclusion and Future Work

CIRL models a robot and human as sharing the goal of maximizing the human’s reward, yielding cooperative learning behavior and a framework for analyzing HRI incentives. Computing an optimal policy pair reduces to a POMDP, while the coordination assumptions motivate future work on how independent actors arrive at mutual best responses.

5 Conclusion and Future Work

  • CIRL has the robot maximize the human’s reward in a shared environment, rather than estimate that reward and adopt it as its own.The model supports cooperative learning and a framework for designing HRI algorithms and analyzing both actors’ incentives.Source: §5 · p. 8
  • Computing an optimal policy pair in CIRL reduces to solving a POMDP, but centralized computation assumes both actors can be programmed to follow a coordination policy.The authors note this is infeasible in reality, though it may help train humans to be better teachers.Source: §5 · p. 8
  • Future research should address how independent actors arrive at policies that are mutual best responses.The authors propose designing machines that provably converge to the right purpose as they go along, rather than putting a specific purpose into the machine.Source: §5 · p. 8

6 Appendix: Supplementary Material & Proofs

The appendix formalizes CIRL as a shared-reward game in which the human knows the reward parameter, and gives structural results for computing optimal policies. It also characterizes apprenticeship CIRL and shows that a human may teach through behavior that violates the expert demonstrator assumption.

6.1 CIRL Formulation

  • CIRL is a two-player Markov game with identical payoffs, where the human observes the static reward parameter and both agents know its prior.The game also specifies world states, each agent’s actions, transitions, a parameterized reward function, an initial distribution, and a discount factor.Source: §6.1 · p. 9
  • Shared rewards incentivize the human to teach and the robot to learn without explicitly encoding those objectives for either agent.Source: §6.1 · p. 9

6.2 Structural Results for Optimal Equilibrium Computation

  • An optimal CIRL policy pair can be computed through a coordination POMDP whose hidden state is S × Θ and whose policies preserve the pair’s discounted reward.CIRL’s private information is limited to the human’s initial observation of θ, allowing the reduction to preserve the hidden-state size.Source: §6.2 · pp. 9–10
  • Optimal human and robot policies can depend only on the current state and the robot’s belief.Source: §6.2 · p. 10

6.3 Apprenticeship CIRL

  • In apprenticeship CIRL, the robot’s optimal deployment policy maximizes reward in the MDP induced by the mean reward parameter.The result applies when the robot receives no further human actions or common observations during deployment.Source: §6.3 · p. 10
  • A human’s best response can violate the expert demonstrator assumption: at θ = 0.49, the human sacrifices immediate reward to signal a preferred robot action.In the example, the human chooses (1, 1) rather than the expert choice (0, 2), because the resulting robot response better matches the human’s preference.Source: §6.3 · p. 11

Related papers

Loading 1606.03137v4…