## Introduction

Two distinct research paradigms have studied how prior tasks or experiences can be used by an agent to inform future learning.

* Meta Learning:  past experience is used to acquire a prior over model parameters or a learning procedure, and typically studies a setting where a set of meta-training tasks are made available together upfront
* Online learning : a sequential setting where tasks are revealed one after another, but aims to attain zero-shot generalization without any task-specific adaptation.

We argue that neither setting is ideal for studying continual lifelong learning. Meta-learning deals with learning to learn, but neglects the sequential and non-stationary aspects of the problem. Online learning offers an appealing theoretical framework, but does not generally consider how past experience can accelerate adaptation to a new task.

## Online Learning

Online learning focuses on regret minimization. Most standard notion of regret is to compare to the cumulative loss of the best fixed model in hindsight:
https://i.imgur.com/pbZG4kK.png
One way minimize regret is with Follow the Leader (FTL):
https://i.imgur.com/NCs73vG.png

## Online Meta-learning Setting:

let $U_t$ be the update procedure for task $t$
e.g. in MAML:
https://i.imgur.com/Q4I4HkD.png


The overall protocol for the setting is as follows:
1. At round t, the agent chooses a model defined by $w_t$
2. The world simultaneously chooses task defined by $f_t$ 
3. The agent obtains access to the update procedure $U_t$, and uses it to update parameters as $\tilde w_t = U_t(w_t)$
4. The agent incurs loss $f_t(\tilde w_t )$. Advance to round t + 1.

the goal for the agent is to minimize regrets over rounds.
Achieving sublinear regrets means you're improving and converging to upper bound (joint training on all tasks)


## Algorithm and Analysis:

Follow the meta-leader (FTML): 
https://i.imgur.com/qWb9g8Q.png

FTML’s regret is sublinear (under some assumption)

# Simultaneous Deep transfer across domains and tasks
## Tzeng, Hoffman, Saenko, 2015

  * The paper aims to exploit unlabeled and sparsely labeled data from the target domain.
  * As a baseline, they mention that one could match feature distributions between source and target domain. This work will also explore correlation between categories, such as _bottle_ and _mug._
  * The authors derive inspiration from the _Name the dataset_ game by Torralbe and Efros. In this game, you train a classifier to predict which dataset an image originates from. This idea transpires into the domain confusion loss. The domain classifier measures the confusion between learned features from source and target domain. The image classifier learns a feature representation that makes the domain inditinguishable, as measured by the domain confusion.
  * The second idea also learns the similarity structure between objects in the target domain. This works as follows. _We first compute the average output probability distribution, or “softlabel,” over the source training examples in each category. Then, for each target labeled example, we directly optimize our model to match the distribution over classes to the soft label. In this way we are able to perform task adaptation by transferring information to categories with no explicit labels in the target domain._
  * The experiments take place in two situations. The _supervised_ case, where only few labels are present in the target domain. The _semi supervised_ case, where only few labels of a subset of the classes are present.  
  * In the final section, the authors perform analysis on theis own result. They show how the image classifier correctly labeled monitor, while no labels for monitor were present in the target domain.

This paper presents a variational approach to the maximisation of mutual information in the context of a reinforcement learning agent. Mutual information in this context can provide a learning signal to the agent that is "intrinsically motivated", because it relies solely on the agent's state/beliefs and does not require from the ("outside") user an explicit definition of rewards.

Specifically, the learning objective, for a current state s, is the mutual information between the sequence of K actions a proposed by an exploration distribution $w(a|s)$ and the final state s' of the agent after performing these actions. To understand what the properties of this objective, it is useful to consider the form of this mutual information as a difference of conditional entropies:

$$I(a,s'|s) = H(a|s) - H(a|s',s)$$

Where $I(.|.)$ is the (conditional) mutual information and $H(.|.)$ is the (conditional) entropy. This objective thus asks that the agent find an exploration distribution that explores as much as possible (i.e. has high $H(a|s)$ entropy) but is such that these actions have predictable consequences (i.e. lead to predictable state s' so that $H(a|s',s)$ is low). So one could think of the agent as trying to learn to have control of as much of the environment as possible, thus this objective has also been coined as "empowerment".

The main contribution of this work is to show how to train, on a large scale (i.e. larger state space and action space) with this objective, using neural networks. They build on a variational lower bound on the mutual information and then derive from it a stochastic variational training algorithm for it. The procedure has 3 components: the exploration distribution $w(a|s)$, the environment $p(s'|s,a)$ (can be thought as an encoder, but which isn't modeled and is only interacted with/sampled from) and the planning model $p(a|s',s)$ (which is modeled and can be thought of as a decoder). The main technical contribution is in how to update the exploration distribution (see section 4.2.2 for the technical details).

This approach exploits neural networks of various forms. Neural autoregressive generative models are also used as models for the exploration distribution as well as the decoder or planning distribution. Interestingly, the framework allows to also learn the state representation s as a function of some "raw" representation x of states. For raw states corresponding to images (e.g. the pixels of the screen image in a game), CNNs are used.

Recently, DeepMind released a new paper showing strong performance on board game tasks using a mechanism similar to the Value Prediction Network one in this paper, which inspired me to go back and get a grounding in this earlier work. 

A goal of this paper is to design a model-based RL approach that can scale to complex environment spaces, but can still be used to run simulations and do explicit planning. Traditional, model-based RL has worked by learning a dynamics model of the environment - predicting the next observation state given the current one and an action, and then using that model of the world to learn values and plan with. In addition to the advantages of explicit planning, a hope is that model-based systems generalize better to new environments, because they predict one-step changes in local dynamics in a way that can be more easily separated from long-term dynamics or reward patterns. 

However, a downside of MBRL is that it can be hard to train, especially when your observation space is high-dimensional, and learning a straight model of your environment will lead to you learning details that aren't actually unimportant for planning or creating policies. 

The synthesis proposed by this paper is the Value Prediction Network. Rather than predicting observed state at the next step, it learns a transition model in latent space, and then learns to predict next-step reward and future value from that latent space vector. Because it learns to encode latent-space state from observations, and also learns a transition model from one latent state to another, the model can be used for planning, by simulating multiple transitions between latent state. However, unlike a normal dynamics model, whose training signal comes from a loss against observational prediction, the signal for training both latent → reward/value/discount predictions, and latent → latent transitions comes from using this pipeline to predict reward values. This means that if an aspect of the environment isn't useful for predicting reward, it won't generally be encoded into latent state, meaning you don't waste model capacity predicting irrelevant detail. 

https://i.imgur.com/4bJylms.png

Once this model exists, it can be used for generating a policy through a tree-search planning approach: simulating future trajectories and aggregating the predicted reward along those trajectories, and then taking the highest-value one. 

The authors find that their model is able to do better than both model-free and model-based methods on the tasks they tested on. In particular, they find that it has many of the benefits of a model that predicts full observations, but that the Value Prediction Network learns more quickly, and is more robust to stochastic environments where there's an inherent ceiling on how well a next-step observation prediction can work. 

My main question coming into this paper is: how is this different from simply a value estimator like those used in DQN or A2C, and my impression is that the difference comes from this model's ability to do explicit state simulation in latent space, and then predict a value off of the *latent* state, whereas a value network predicts value from observational state.

This paper proposes to learn features for images using neural networks that predict the relative motion of the camera that captured two successive images. The main motivation for this approach is that such data would be very cheap to collect, as it would not require any labelling by a human and only relies on "egomotion" (and thus readily available) information. More concretely, what must be predicted is the X/Y/Z rotation or translation movements. This is converted into a classification problem by binning each movement into a fixed number of ranges of movement magnitude. The neural network architecture then consists in a siamese-style CNN (SCNN). First two Base-CNN (BCNN) with tied weights process the input image pair (one image per BCNN) to produce features for each image. These features are then concatenated and fed to a Top-CNN (TCNN) which produces a prediction for the relative transformation that relates the two images. The output layer thus contains groups of softmax units, one for each dimension of variation of the transformation (e.g. 3 for X/Y/Z rotation). 

The experiments show that pretraining on this task is competitive with pretraining a CNN on the same amount of ImageNet classification data.