Paper:
Exploration while learning representations is one of the main challenges Deep Reinforcement Learning (DRL) faces today. As the learned representation is dependant in the observed data, the exploration strategy has a crucial role. The popular DQN algorithm has improved significantly the capabilities of Reinforcement Learning (RL) algorithms to learn state representations from raw data, yet, it uses a naive exploration strategy which is statistically inefficient. The Randomized Least Squares Value Iteration (RLSVI) algorithm (Osband et al., 2016), on the other hand, explores and generalizes efficiently via linearly parameterized value functions. However, it is based on hand-designed state representation that requires prior engineering work for every environment. In this paper, we propose a Deep Learning adaptation for RLSVI. Rather than using hand-design state representation, we use a state representation that is being learned directly from the data by a DQN agent. As the representation is being optimized during the learning process, a key component for the suggested method is a likelihood matching mechanism, which adapts to the changing representations. We demonstrate the importance of the various properties of our algorithm on a toy problem and show that our method outperforms DQN in five Atari benchmarks, reaching competitive results with the Rainbow algorithm.

Review:
The paper proposes to extend the popular linear-control algorithm, RLSVI, to utilize learned representations. This is done by adapting a work from bandit literature that utilizes BLR with representations that are learned via a DNN. The proposed solution is then compared to DQN with fixed epsilon as the exploration strategy in a chain MDP, and to the Rainbow agent and DQN in 5 selected Atari games to show sample-efficiency improvements.
The idea presented by the work is interesting, and utilizing a complete Bayesian Linear Regression framework (variable variance, as opposed to fixed variance in the prior) does sound appealing in terms of adaptability - as it is what the authors argue for, as being key to their proposal. But the work in the paper is not in an acceptable form due to the following key reasons: (1) the presentation of the ideas and the algorithm, "despite the lack of theoretical guarantees" is hard to understand, (2) the DQN baseline compared to (definitely in the Augmented Chain Environment, and possibly in the Atari games), are based on a fixed epsilon exploration strategy whereas DQN as proposed uses a epsilon-annealing strategy for exploration, (3) the baselines compared to are not comprehensive, (4) generally the paper is rather unpolished.
Following are main points of feedback, regarding which I would like to know the authors opinions/responses in the rebuttal if possible. After that, are some concrete questions to clarify the contents of the paper.
Feedback:
(1) the linear contextual bandit work the paper is built on is currently under review at ICLR 2020. While this should not be the reason for rejection, the idea of likelihood matching as motivated from that bandit work does not simply transfer to the RL case. For instance, based on the pseudocode in the paper (and the provided explanation), after likelihood matching is done, the new BLR updates still seem to use the old representations and targets (as the target net update is done after the loop). This is possibly a typo, or something deeper is left unexplained here.
(2) While it is true that the BDQN work does not utilize the last layer of their weights, and is built on the DDQN algorithm, I think they still are a reasonable baseline as the key idea distinguishing the two is variable variance prior vs. a fixed variance prior. While I understand having all the baseline experiments from the exploration in deep RL literature is hard as it is quite vast - Bootstrap DQN, UBE, Bootstrap Prior - I think the closest baseline has to be BDQN to your proposal and therefore is a natural competitor.
(3) DDQN has been shown to be reducing the overestimation bias prevalent in DQN and therefore was the framework BDQN was built on. Why do you choose to use DQN instead of DDQN? A discussion regarding this seems a natural part of the paper.
(4) Are the benefits of adaptive sigma present if the base algorithm is changed to DDQN? I think this is an important point of discussion/analysis. It does not have to outperform DDQN, but even a comparative study empirically would be an insightful and comprehensive contribution.
(5) I assume that the likelihood utilizes the inverse of the covariance as opposed to the covariance -- something that seems amiss in the current write-up.
(6) Isn't S_i in Section 4.3 already a scalar? Why is there a trace of a scalar?
(7) Section 5.1.3 -- the version that does not match likelihood is not BDQN as it is built on DDQN -- presumable significant regret differences.
Questions:
(1) DQN as proposed is with annealed e-greedy. Are the experiments in Augmented Chain Environment utilizing this or a fixed e-greedy strategy?
(2) What exactly is the connection between catastrophic forgetting and likelihood matching in the policy improvement context? Why should an improved policy match the likelihood of features as learned by an older policy?
(3) Why choose to sample a set of value functions instead of sampling every timestep? Only because sampling is expensive or does it provide any stability?
(4) Why did you pick these 5 Atari games?
Given the algorithm is a particular design choice, and the argument for its utility is empirical, I definitely think the design choice needs to be discussed more thoroughly, and the manuscript currently does not do that. While empirical experiments in the Atari suite can be hard ask depending on the availability of computational resources, I think the work algorithmic choices made here are left undiscussed and the empirical results aren't really convincing. Further, the presentation is rather imprecise and error-ridden. Therefore, I do not think the work can be accepted.
There are many imprecise statements and typos in the paper, which are listed here to aid the future versions:
(1) Please review your psuedocode based on comment (1) in Feedback.
(2) The content in the Introduction does not make a note of many algorithms proposed for exploration in Deep RL -- UBE [1], Bootstrap DQN [2], Randomized prior for Bootstrap DQN [3], Parameter noise[4].
(3) Section 2, para 2 -- Recent work (Osband --> Recent works (Osband
(4) Section 2, para 3 -- acts greedy --> acts greedily
(5) Section 3, para 1 -- gamma in (0,1) --> [0,1]
(6) Section 3, para 1 -- survey --> review
(7) Section 3.1, para 1 -- acts the greedy action according to the --> acts greedily wrt
(8) Section 4.1, buffer consists of gamma/termination flag
(9) Section 4.2, para 1 -- First, rather than solving .. -- so did RLSVI. I guess you mean the regression problem is not solved every tilmestep.
(10) Section 4.2 last sentence -- please expand why that assumption is good?
(11) opening inverted commas everywhere.
(12) Section 5.1.4, last sentence -- grammar.
(13) Footnote 1 and content in Section 5.2 "we used publicly available learning curves" are contradictory.
[1] O'Donoghue, Brendan, et al. "The uncertainty bellman equation and exploration." arXiv preprint arXiv:1709.05380 (2017).
[2] Osband, Ian, et al. "Deep exploration via bootstrapped DQN." Advances in neural information processing systems. 2016.
[3] Osband, Ian, John Aslanides, and Albin Cassirer. "Randomized prior functions for deep reinforcement learning." Advances in Neural Information Processing Systems. 2018.
[4] Plappert, Matthias, et al. "Parameter space noise for exploration." arXiv preprint arXiv:1706.01905 (2017).