This is not a detailed summary, just general notes:

Authors make a excellent and extensive comparison of Model Free, Model based methods in 18 environments. In general, the authors compare 3 classes of Model Based Reinforcement Learning (MBRL) algorithms using as metric for comparison the total return in the environment after 200K steps (reporting the mean and std by taking windows of 5000 steps throughout the whole training - and averaging across 4 seeds for each algorithm). They compare MBRL classes:

- **Dyna style:** using a policy to gather data, training a transition function model on this data(i.e. dynamics function / "world model"), and using data predicted by the model (i.e. "imaginary" data) to train the policy)

- **Policy Search with Backpropagation through Time (BPTT):** starting at some state $s_0$ the policy rolls out an episode using the model. Then given the trajectory and its sum of rewards (or any other objective function to maximize) one can differentiate this expression with respect to the policies parameters $\theta$
 to obtain the gradient. The training process iterates between collecting data using the current policy and improving the policy via computing the BPTT gradient ... Some version include dynamic programming approaches where the ground -truth dynamics need to be known

- **Model Predictive Control (MPC) / Shooting methods:** There is in general no explicit policy to choose actions, rather the actions sequence is chosen by: starting with a set of candidates of actions sequences $a_{t:t+\tau}$ , propagating this actions sequences in the dynamics model, and then choosing the action sequence which achieved the highest return through out the propagated episode. Then, the agent only applies the first action from the optimal sequence and re-plans at every time-step.

They also compare this to Model Free (MF) methods such as SAC and TD3.

**Brief conclusions which I noticed from MB and MF comparisons:** (note the $>$
 indicates better than )

- **MF:** SAC & TD3 $>$ PPO & TRPO

- **Performance:** MPC (shooting, robust performance except for complex env.) $>$ Dyna (bad for long H) $>$ BPTT (SVG very good for complex env.)

- **State and Action Noise:** MPC (shooting, re-planning compensates for noise) $>$ Dyna (lots of Model predictive errors … although meta learning actually benefits from noisy do to lack of exploration)

- **MB dynamics error accumulation:** MB performance plateaus, more data $\neq$ better performance $\rightarrow$ 1. prediction error accumulates through time 2. As we the policy and model improvement are closely link, we can (early) fall into local minima

- **Early Termination (ET):** including ET always negatively affects MB methods. Different ways of incorporating ET into planning horizon (see appendix G for details) work better for some environment but worst for more complex envs. - so, tbh theres no conclusion to be made about early termination schemes (same as for there entire paper :D, but it's not the authors fault, is just the (sad) direction in which most RL / DL research is moving in)

**Some stuff which seems counterintuitive:**

- Why can’t we see a significant sample efficiency of MB w.r.t to MF ?
- Why does PILCO suck at almost everything ? original authors/ implementation seems to excel at several tasks
- When using ensembles (e.g. PETS), why is predicting the next state as the Expectation over the ensemble (PE-E: $\boldsymbol{s}_{t+1}=\mathbb{E}\left[\widetilde{f}_{\boldsymbol{\theta}}\left(\boldsymbol{s}_{t}, \boldsymbol{a}_{t}\right)\right]$) better or at least highly comparable to propagating a particle by leveraging the ensemble of models (PE-TS: given $P$ initial states $\boldsymbol{s}_{t=0}^{p}=\boldsymbol{s}_{0} \forall \boldsymbol{p}$, propagate each state / particle $p$ using *one* model $b(p)$ from the entire ensemble ($B$), such that $\boldsymbol{s}_{t+1}^{p} \sim \tilde{f}_{\boldsymbol{\theta}_{b(p)}}\left(\boldsymbol{s}_{t}^{\boldsymbol{p}}, \boldsymbol{a}_{t}\right)$ ), which should in theory better capture uncertainty / multimodality of the State space ??

The paper discusses and empirically investigates by empirical testing the effect of "catastrophic forgetting" (**CF**), i.e. the inability of a model to perform a task it was previously trained to perform if retrained to perform a second task. 

An illuminating example is what happens in ML systems with convex objectives: regardless of the initialization (i.e. of what was learnt by doing the first task), the training of the second task will always end in the global minimum, thus totally "forgetting" the first one. 

Neuroscientific evidence (and common sense) suggest that the outcome of the experiment is deeply influenced by the similarity of the tasks involved. Namely, if (i) the two tasks are *functionally identical but input is presented in a different format* or if (ii)  *tasks are similar* and the third case for (iii) *dissimilar tasks*. 

Relevant examples may be provided respectively by (i) performing the same image classification task starting from two different image representations as RGB or HSL, (ii) performing image classification tasks with semantically similar as classifying two similar animals and (iii) performing a text classification followed by image classification. 

The problem is investigated by an empirical study covering two methods of training ("SGD" and "dropout") combined with 4 activations functions (logistic sigmoid, RELU, LWTA, Maxout). A random search is carried out on these parameters. 

From a practitioner's point of view, it is interesting to note that dropout has been set to 0.5 in hidden units and 0.2 in the visible one since this is a reasonably well-known parameter. 

## Why the paper is important
It is apparently the first to provide a systematic empirical analysis of CF. Establishes a framework and baselines to face the problem.

## Key conclusions, takeaways and modelling remarks
* dropout helps in preventing CF
* dropout seems to increase the optimal model size with respect to the model without dropout 
* choice of activation function has a less consistent effect than dropout\no dropout choice
* dissimilar task experiment provides a  notable exception of then dissimilar task experiment
* the previous hypothesis that LWTA activation is particularly resistant to CF is rejected  (even if it performs best in the new task in the dissimilar task pair the behaviour is inconsistent)
* choice of activation function should always be cross-validated
* If computational resources are insufficient for cross-validation the combination dropout + maxout activation function is recommended.

The paper proposes a method to perform joint instance and semantic segmentation. The method is fast as it is meant to run in an embedded environment (such as a robot). While the semantic map may seem redundant given the instance one, it is not as semantic segmentation is a key part of obtaining the instance map.

# Architecture

![image](https://user-images.githubusercontent.com/8659132/63187959-24cdb380-c02e-11e9-9121-77e0923e91c6.png)

The image is first put through a typical CNN encoder (specifically a ResNet derivative), followed by 3 separate decoders. The output of the decoder is at a low resolution for faster processing.

Decoders:
- Semantic segmentation: coupled with the encoder, it's U-Net-like. The output is a segmentation map.
- Instance center: for each pixel, outputs the confidence that it is the center of an object.
- Embedding: for each pixel, computes a 32 dimensional embedding. This embedding must have a low distance to embedding of other pixels of the same instance, and high distance to embedding of other pixels.

To obtain the instance map, the segmentation map is used to mask the other 2 decoder outputs to separate the embeddings and centers of each class. Centers are thresholded at 0.7, and centers with embedding distances lower than a set amount are discarded, as they are considered duplicates.

Then for each class, a similarity matrix is computed between all pixels from that class and centers from that class. Pixels are assigned to their closest centers, which represent different instances of the class.

Finally, the segmentation and instance maps are upsampled using the SLIC algorithm.

# Loss

There is one loss for each decoder head.
- Semantic segmentation: weighted cross-entropy
- Instance center: cross-entropy term modulated by a $\gamma$ parameter to counter the over-representation of the background over the target classes.
![image](https://user-images.githubusercontent.com/8659132/63286485-22659680-c286-11e9-9134-f1b823a34217.png)

- Embedding: composed of 3 parts, an attracting force between embeddings of the same instance, a repelling force between embeddings of different instances, and a l2 regularization on the embedding.
![image](https://user-images.githubusercontent.com/8659132/63286399-f1856180-c285-11e9-9136-feb6c4a555e5.png)
![image](https://user-images.githubusercontent.com/8659132/63286411-fcd88d00-c285-11e9-939f-0771579d8263.png)
$\hat{e}$ are the embeddings, $\delta_a$ is an hyper-parameter defining "close enough", and $\delta_b$ defines "far enough"

The whole model is trained jointly using a weighted sum of the 3 losses.

# Experiments and results

The authors test their method on the Cityscape dataset, which is composed of 5000 annotated images and 8 instance classes. They compare their methods both for semantic segmentation and instance segmentation.

![image](https://user-images.githubusercontent.com/8659132/63287573-a882dc80-c288-11e9-83e0-b352e43bdf28.png)

For semantic segmentation, their method is ok, though ENet for example performs better on average and is much faster.

![image](https://user-images.githubusercontent.com/8659132/63287643-d700b780-c288-11e9-9d40-5bcaf695a744.png)

On the other hand, for instance segmentation, their method is much faster than the other while still performing well. Not SOTA on performance, but considering the real-time constraint, it's much better.

# Comments

- Most instance segmentation methods tend to be sluggish and overly complicated. This approach is much more elegant in my opinion.
- If they removed the aggressive down/up sampling, I wonder if they would beat MaskRCNN and PANet.
- I'm not sure what's the point of upsampling the semantic map given that we already have the instance map.

Disclaimer: I am an author

# Intro

Experience replay (ER) and generative replay (GEN) are two effective continual learning strategies. In the former, samples from a stored memory are replayed to the continual learner to reduce forgetting. In the latter, old data is compressed with a generative model and generated data is replayed to the continual learner. Both of these strategies assume a random sampling of the memories. But learning a new task doesn't cause **equal** interference (forgetting) on the previous tasks!  

In this work, we propose a controlled sampling of the replays. Specifically, we retrieve the samples which are most interfered, i.e. whose prediction will be most negatively impacted by the foreseen parameters update. The method is called Maximally Interfered Retrieval (MIR).

## Cartoon for explanation

https://i.imgur.com/5F3jT36.png

Learning about dogs and horses might cause more interference on lions and zebras than on cars and oranges. Thus, replaying lions and zebras would be a more efficient strategy.

# Method

1) incoming data: $(X_t,Y_t)$

2) foreseen parameter update: $\theta^v= \theta-\alpha\nabla\mathcal{L}(f_\theta(X_t),Y_t)$

### applied to ER (ER-MIR)
3) Search for the top-$k$ values $x$ in the stored memories using the criterion $$s_{MI}(x) = \mathcal{L}(f_{\theta^v}(x),y) -\mathcal{L}(f_{\theta}(x),y)$$

### or applied to GEN (GEN-MIR)
3)   
$$
     \underset{Z}{\max} \, \mathcal{L}\big(f_{\theta^v}(g_\gamma(Z)),Y^*\big) -\mathcal{L}\big(f_{\theta}(g_\gamma(Z)),Y^*\big)
$$
$$
         \text{s.t.}   \quad ||z_i-z_j||_2^2 > \epsilon \forall  z_i,z_j \in Z \,\text{with} \, z_i\neq z_j
$$
i.e. search in the latent space of a generative model $g_\gamma$ for samples that are the most forgotten given the foreseen update.

4) Then add theses memories to incoming data $X_t$ and train $f_\theta$

# Results

### qualitative
https://i.imgur.com/ZRNTWXe.png

Whilst learning 8s and 9s (first row), GEN-MIR mainly retrieves 3s and 4s (bottom two rows) which are similar to 8s and 9s respectively.

### quantitative 

GEN-MIR was tested on MNIST SPLIT and Permuted MNIST, outperforming the baselines in both cases.

ER-MIR was tested on MNIST SPLIT, Permuted MNIST and Split CIFAR-10, outperforming the baselines in all cases.


# Other stuff
### (for avid readers)

We propose a hybrid method (AE-MIR) in which the generative model is replaced with an autoencoder to facilitate the compression of harder dataset like e.g. CIFAR-10.

### Summary
Knowing when a model is qualified to make a prediction is critical to safe deployment of ML technology. Model-independent / Unsupervised Out-of-Distribution (OoD) detection is appealing mostly because it doesn't require task-specific labels to train. It is tempting to suggest a simple one-tailed test in which lower likelihoods are OoD (assigned by a Likelihood Model), but the intuition that In-Distribution (ID) inputs should have highest likelihoods _does not hold in higher dimension_. The authors propose to use the Watanabe-Akaike Information Criterion (WAIC) to circumvent this problem and empirically show the robustness of the approach.

### Counterintuitive Properties of Likelihood Models:
https://i.imgur.com/4vo0Ff5.png
So a GLOW model with Gaussian prior maps SVHN closer to the origin than Cifar (but never actually generates SVHN because Gaussian samples are on the shell). This is bad news for OoD detection.

### Proposed Methodology:
Use the WAIC criterion for OoD detection which gives an asymptotically correct estimate of the gap between the training set and test set expectations:
https://i.imgur.com/vasSxuk.png
Basically,  the correction term subtracts the variance in likelihoods across independent samples from the posterior. This acts to robustify the estimate, ensuring that points that are sensitive to the particular choice of posterior are penalized. They use an ensemble of generative models as a proxy for posterior samples i.e. the ensembles acts as approximate posterior samples.
Now, OoD can be detected with a Likelihood Model:
https://i.imgur.com/M3CDKOA.png
### Discussion
Interestingly, GLOW maps Cifar and other datasets INSIDE the gaussian shell (which is an annulus of radius $\sqrt{dim} = \sqrt{3072} \approx 55.4$
https://i.imgur.com/ERdgOaz.png
This is in itself quite disturbing, as it suggests that better flow-based generative models (for sampling) can be obtained by encouraging the training distribution to overlap better with the typical set in latent
space.