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Title: SMiRL: Surprise Minimizing RL in Entropic Environments

Paper content:
All living organisms struggle against the forces of nature to carve out niches where
they can maintain relative stasis.
We propose that such a search for order amidst
chaos might offer a unifying principle for the emergence of useful behaviors in
artificial agents.
We formalize this idea into an unsupervised reinforcement learning
method called surprise minimizing RL (SMiRL).
SMiRL trains an agent with the
objective of maximizing the probability of observed states under a model trained on
all previously seen states.
The resulting agents acquire several proactive behaviors
to seek and maintain stable states such as balancing and damage avoidance, that
are closely tied to the affordances of the environment and its prevailing sources
of entropy, such as winds, earthquakes, and other agents.
We demonstrate that
our surprise minimizing agents can successfully play Tetris, Doom, and control
a  humanoid  to  avoid  falls,  without  any  task-specific  reward  supervision.
We
further show that SMiRL can be used as an unsupervised pre-training objective
that substantially accelerates subsequent reward-driven learning
The general struggle for existence of animate beings is not a struggle for raw materials, nor for energy, but a struggle for negative entropy.
(Ludwig Boltzmann, 1886)
All living organisms carve out environmental niches within which they can maintain relative predictability amidst the ever-increasing entropy around them (Boltzmann, 1886; Schrödinger, 1944; Schneider & Kay, 1994; Friston, 2009) .
Humans, for example, go to great lengths to shield themselves from surprise -we band together in millions to build cities with homes, supplying water, food, gas, and electricity to control the deterioration of our bodies and living spaces amidst heat and cold, wind and storm.
The need to discover and maintain such surprise-free equilibria has driven great resourcefulness and skill in organisms across very diverse natural habitats.
Motivated by this, we ask: could the motive of preserving order amidst chaos guide the automatic acquisition of useful behaviors in artificial agents?
Our method therefore addresses the unsupervised reinforcement learning problem: how might an agent in an environment acquire complex behaviors and skills with no external supervision?
This central problem in artificial intelligence has evoked several candidate solutions, largely focusing on novelty-seeking behaviors (Schmidhuber, 1991; Lehman & Stanley, 2011; Still & Precup, 2012; Bellemare et al., 2016; Houthooft et al., 2016; Pathak et al., 2017) .
In simulated worlds, such as video games, novelty-seeking intrinsic motivation can lead to interesting and meaningful behavior.
However, we argue that these sterile environments are fundamentally lacking compared to the real world.
In the real world, natural forces and other agents offer bountiful novelty.
The second law of thermodynamics stipulates ever-increasing entropy, and therefore perpetual novelty, without even requiring any agent intervention.
Instead, the challenge in natural environments is homeostasis: discovering behaviors that enable agents to maintain an equilibrium, for example to preserve their bodies, their homes, and avoid predators and hunger.
Even novelty seeking behaviors may emerge naturally as a means to maintain homeostasis: an agent that is curious and forages for food in unlikely places might better satisfy its hunger.
In natural environments (left), an inactive agent will experience a wide variety of states.
By reasoning about future surprise, a SMiRL agent can take actions that temporarily increase surprise but reduce it in the long term.
For example, building a house initially results in novel states, but once it is built, the house allows the agent to experience a more stable and surprise-free environment.
On the right we show an interpretation of the agent interaction loop using SMiRL.
When the agent observes a state, it updates it belief p(s) over states.
Then, the action policy π(a|s, θ) is conditioned on this belief and maximizes the expected likelihood of the next state under its belief.
We formalize allostasis as an objective for reinforcement learning based on surprise minimization (SMiRL).
In highly entropic and dynamic environments with undesirable forms of novelty, minimizing surprise (i.e., minimizing novelty) causes agents to naturally seek a stable equilibrium.
Natural environments with winds, earthquakes, adversaries, and other disruptions already offer a steady stream of novel stimuli, and an agent that minimizes surprise in these environments will act and explore in order to find the means to maintain a stable equilibrium in the face of these disturbances.
SMiRL is simple to describe and implement: it works by maintaining a density p(s) of visited states and training a policy to act such that future states have high likelihood under p(s).
This interaction scheme is shown in Figure 1 (right) Across many different environments, with varied disruptive forces, and in agents with diverse embodiments and action spaces, we show that this simple approach induces useful equilibrium-seeking behaviors.
We show that SMiRL agents can solve Tetris, avoid fireballs in Doom, and enable a simulated humanoid to balance and locomote, without any explicit task reward.
More pragmatically, we show that SMiRL can be used together with a task reward to accelerate standard reinforcement learning in dynamic environments, and can provide a simple mechanism for imitation learning.
SMiRL holds promise for a new kind of unsupervised RL method that produces behaviors that are closely tied to the prevailing disruptive forces, adversaries, and other sources of entropy in the environment.
Videos of our results are available at https://sites.google.com/view/surpriseminimization
We presented an unsupervised reinforcement learning method based on minimization of surprise.
We show that surprise minimization can be used to learn a variety of behaviors that maintain "homeostasis," putting the agent into stable and sustainable limit cycles in its environment.
Across a range of tasks, these stable limit cycles correspond to useful, semantically meaningful, and complex behaviors: clearing rows in Tetris, avoiding fireballs in VizDoom, and learning to balance and hop forward with a bipedal robot.
The key insight utilized by our method is that, in contrast to simple simulated domains, realistic environments exhibit dynamic phenomena that gradually increase entropy over time.
An agent that resists this growth in entropy must take active and coordinated actions, thus learning increasingly complex behaviors.
This stands in stark contrast to commonly proposed intrinsic exploration methods based on novelty, which instead seek to visit novel states and increase entropy.
Besides fully unsupervised reinforcement learning, where we show that our method can give rise to intelligent and complex policies, we also illustrate several more pragmatic applications of our approach.
We show that surprise minimization can provide a general-purpose risk aversion reward that, when combined with task rewards, can improve learning in environments where avoiding catastrophic (and surprising) outcomes is desirable.
We also show that SMiRL can be adapted to perform a rudimentary form of imitation.
Our investigation of surprise minimization suggests a number of directions for future work.
The particular behavior of a surprise minimizing agent is strongly influenced by the particular choice of state representation: by including or excluding particular observation modalities, the agent will be more or less surprised.
where s is a single state, θ i is the sample mean calculated from D t indicating the proportion of datapoints where location i has been occupied by a block, and s i is a binary variable indicating the presence of a block at location i.
If the blocks stack to the top, the game board resets, but the episode continues and the dataset D t continues to accumulate states.
SMiRL on VizDoom and Humanoid.
In these environments the observations placed in the buffer are downsampled 10 × 13 single-frame observations for VizDoom environments and the full state for the Humanoid environments.
We model p(s) as an independent Gaussian distribution for each dimension in the observation.
Then, the SMiRL reward can be computed as:
where s is a single state, µ i and σ i are calculated as the sample mean and standard deviation from D t and s i is the i th observation feature of s.

assistant: text: Learning emergent behavior by minimizing Bayesian surprise with RL in natural environments with entropy.