
Submitted by Assigned_Reviewer_1
Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The problem formulation (Sec.2) was new to me, though the proposed approach (Sec.3) draws on some standard methodology for inference in graphical models (i.e. EM, Viterbi).
For such a conventional algorithm to have impact, I would expect to see a compelling application of the new model.
The empirical analysis presents results for two small simulated grid words, which confirm good performance, but don't provide compelling evidence that the new model is justified.
Some of the challenges of EM (e.g. convergence to local optimum, initialization, picking the number of reward functions) are not discussed  did this never occur in the experiments?
The third experiment uses realworld taxi trajectories, yet I don't quite understand why it's better to infer two separate reward functions, rather than incorporate the speed (which is the main feature in the reward transition function) directly in the reward parameterization (theta).
Following the author response: The response did clarify one misconception I had about the setting for the 3rd experiment (regarding whether the taxi speed should be incorporated as a reward variable). This improved my appreciation for the paper's motivation and setting.
Q2: Please summarize your review in 12 sentences
The paper tackles the problem of IRL from multiple reward functions.
I had some doubts about the problem setting, though the discussion and other reviews raised some interesting points in support of this.
The algorithmic approach is wellmotivated, and clearly explained, however I did not see anything new in this aspect.
Submitted by Assigned_Reviewer_2
Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
This paper addresses the problem of inverse reinforcement learning when the agent can change it's objective during the recording of trajectories. This results in a transition between several reward functions that explain only locally the trajectory of the observed agent. Transition probabilities between reward functions are unknown. The author propose a cascade of an EM and Viterbi algorithms to discover the reward functions and the segments on which they are valid.
The paper is quite well written. Yet the state of the art about IRL stops in 2012. There has been quite a lot of work since then and I'm a bit surprised that the authors didn't think it was worth mentioning recent works (especially those that do not require to solve MDPs iteratively).
The authors propose a very complex model to address the problem at sight and I'm not sure it is worth to make this effort. Indeed, if I understood correctly, the number of reward functions has to be known in advance to run the EM algorithm. Therefore, I don't see why this problem cannot be modelled by adding a dimension to the state space for the index of the current reward function. As the reward function is not observable, this is a hidden variable which makes the problem to be modelled as a POMDP. But there are methods for IRL in POMDPs.
Also, the use of the Viterbi algorithm implies that the transition probabilities between states are known. This constrains even more the setting and makes it usable in very few situations.
Finally, this method can only be used for analysing the behaviour of an agent but not really to find an optimal control for the environment. To me, this actually means that a special care has to be taken to ensure that the learnt reward functions will be interpretable by a human. This is not mentioned in the paper but it is a quite important issue. When the state space is multidimensional, it is very hard to represent the reward function unless it is very sparse for instance. So how would the authors add constraints in this model to be sure to enable the analysis of the behaviour from the learnt reward?
Q2: Please summarize your review in 12 sentences
Globally, I think the proposed model is too complex with respect to the targeted problem and the algorithms used are too restrictive to make this model applicable to real world problems.
Submitted by Assigned_Reviewer_3
Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The authors propose an IRL method that learns locally consistent reward functions from expert demonstrations. To do so, they suppose the existence of a transition function for switching between reward functions which depends on the rewards and the current state and allows them to build a graphical model of their problem.
Their algorithm consists in maximizing the loglikelihood of the expert's demonstrated trajectories depending on some parameters which are the original distributions of states and rewards, the local rewards and the transition function between rewards. To do so, they use the expectationmaximisation (EM) method. Then, via the Viterbi algorithm, they are able to partition the trajectories into segments with local consistent rewards.
Strengths of the paper:
1. The authors leverage existing and classical methods from the machine learning and optimization fields such as EM, Viterbi, Value iteration and gradient ascent in order to build their algorithm. This will allow the community to easily reproduce their results. 2. The experiments are conducted on synthetic and realworld data. They compare their method to MLIRL which does not use locally consistent rewards and which is the canonical choice to compare to as their algorithm is a generalization of MLIRL. The results presented show the superiority of their method over MLIRL. 3. The idea presented by the authors is original as far as I know.
Weaknesses of the paper:
1. The paper is very dense ( the figures are incorporated in the text) which makes the reading difficult. 2. The algorithm proposed needs the knowledge of the dynamics and the number of rewards. The authors, as future works, plan to extend their algorithm to unknown number of rewards, however they do not mention to get rid off the knowledge of the dynamics. Could the authors comment on that as some IRL algorithms do not need a perfect knowledge of the dynamics?
3. The method needs to solve iteratively MDPs when learning the reward functions. For each theta in the gradient ascent a MDP needs to be solved. Is this prohibitive for huge MDPs? Is there a way to avoid that step? The actionvalue function Q is defined via a softmax operator in order to have a derivable policy, does it allow to solve more efficiently the MDP? 4. The authors are using gradient ascent in the EM method, could they comment on the concavity of their criteria? 5. In the experiments (gridworlds), the number of features for the states is very small and thus it is understandable that a reward which is linear on the features will perform badly. Do the authors consider comparing their method to an IRL method where the number of features defining the states is greater? This is the main problem that I have with the experiments, the features used are not expressive enough to consider using a classical IRL method and this can explain why MLIRL performs badly and that its performance does not improve when the number of expert trajectories grows. 6. The performance is measured by the average loglikelihood of the expert's demonstrated trajectories which is the criterion maximized by the algorithm. I think that a more pertinent measure would be the value function of the policy produced by the optimization of the reward obtained by the algorithm. Could the authors comment on that and explain why their performance metric is more appropriate?
Summary: This paper presents a new idea consisting in learning locally consistent rewards in order to solve the IRL problem. The method is original and relies on classical machine learning methods. However, I have some concerns on the efficiency of the method for large MDPs and when the dynamics is not provided.
Q2: Please summarize your review in 12 sentences
This paper presents a new idea consisting in learning locally consistent rewards in order to solve the IRL problem. The method is original and relies on classical machine learning methods. However, I have some concerns on the efficiency of the method for large MDPs and when the dynamics is not provided.
Submitted by Assigned_Reviewer_4
Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The paper proposes not assuming that even with IRL that there is one reward function but different parts of the state space.
in terms of the empirical results I wonder what would happen with fig 5 a with infinite data as well as the the impact on extracting optimal policies. So wouldn't the MLIRL with multiple intentions with enough data and enough underlying rewards would produce similar results?
How worse off, computationally, will the algorithm be against one that just assumes a single reward per trajectory if then you choose a # of reward number greater than 1 but actually there was only one reward?
How would one also protect against overfitting in this case, especially with the increase in parameters?
Q2: Please summarize your review in 12 sentences
An interesting approach to IRL, further breaking possible paths as having different motivations (rewards).
Q1:Author
rebuttal: Please respond to any concerns raised in the reviews. There are
no constraints on how you want to argue your case, except for the fact
that your text should be limited to a maximum of 5000 characters. Note
however, that reviewers and area chairs are busy and may not read long
vague rebuttals. It is in your own interest to be concise and to the
point.
We thank all reviewers for their feedback, which
will be considered when revising our paper.
Reviewer1
We
explained in lines 9295,142144 that by representing the index of reward
function as latent state component in POMDP, its observation model cannot
be easily specified nor learned from expert's trajectories of states,
actions & varphi_s, which invalidates the use of IRL for
POMDP[4].
The state transition probabilities are assumed to be
known as we want to focus on learning the reward functions & their
transitions, which is the core of IRL. Our approach can be easily
extended to learn the unknown state transitions by modeling with a
logistic model and optimizing the last term (5) in EM's Q
function. Another option is to learn the state transitions separately
by counting the frequency of next state given the current state and action
using the (state, action, next state) tuples from experts'
trajectories.
Besides analyzing agent's behavior, our algorithm can
find optimal control. For example, in taxi experiment, we can use the
learned model to produce preferred route choices to guide drivers. To
enable behavior analysis, the Viterbi algorithm identifies states where
experts are likely to switch between reward functions; such states can be
investigated for the resulting causes (lines 99103). Regarding the reward
function, similar to existing IRL algorithms, we assume linear combination
of state features (line 114) & the weights represent preference over
features.
Reviewer2
2. Our approach can be easily extended
to learn the state transition dynamics by modeling with a logistic model
and optimizing the last term (5) in EM's Q function. Another option is
to learn the state transitions separately by counting the frequency of
next state given the current state and action using the (state, action,
next state) tuples from experts' trajectories.
3. Our EM can use an
MDP solution if it yields a stochastic policy differentiable wrt theta.
Softmax is one such option that we used. Another option is the linearly
solvable MDP (LMDP) that is more efficient than standard iterative MDP
solvers. This class includes max entropy IRL, which is empirically shown
in [2] to be outperformed by MLIRL, hence explaining our choice. We
observe that our EM can use LMDP as its policy is stochastic and
differentiable.
4. It is possible for EM to reach local maxima. So,
for each experiment, we run 15 initializations and choose the best result
based on EM's Q function.
5. We agree that in some cases, by
increasing the number of features, a single reward function is enough to
explain the expert's behavior. But, we focus on problems where no single
reward function can explain the entire expert's trajectory, which
motivates the need of multiple locally consistent reward functions (lines
7678). Experiments are tailored to address this.
6. If we
understand your proposed performance measure correctly, it requires the
true reward functions, which are often not available in realworld
datasets. In contrast, our metric directly uses the available demonstrated
trajectories only.
Reviewer3
MLIRL with multiple intentions
and enough data and reward functions cannot produce same results as our
algorithm if the expert switches between reward functions within a
demonstrated trajectory. This is because it does not allow reward function
to switch within a trajectory, while ours does (lines 295304,322323).
But, if the expert does not change his intention within a trajectory,
MLIRL with multiple intentions is equivalent to our
algorithm.
Supposing we compare with MLIRL using one reward
function, our algorithm with multiple reward functions incurs most time in
solving MDPs. So, its incurred time increases linearly in number of reward
functions.
Model complexity is determined by number of reward
functions, which can be controlled to reduce overfitting. A better
solution (future work) is to use a Bayesian nonparametric approach to
learn the number of reward functions from data (line
429).
Reviewer4
We faced the local optimum issue. So, we
initialize 15 times for each experiment and choose best result based on EM
Qfunction. In taxi experiment, we tried 3 reward functions initially, but
2 are similar. Thus, we reduce to 2. A better solution (future work) is to
use a Bayesian nonparametric approach to learn the number of reward
functions from data (line 429).
Expert driver can only observe its
taxi speed while traveling along that road. Without prior taxi speed
information over all states, the expert cannot exploit it within MDP
planning. So, we use taxi speed as the feature affecting reward function
switching during execution, but not the feature constituting the reward
functions (see Remark 1).
Reviewer5 The gradient of MDP Q
function is computed based on a recursive equation by assuming softmax
operation for its policy. Yes, we have to compute optimal policy for each
reward function. 
