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Emergent Behavior by Minimizing Chaos

All living organisms carve out environmental niches within which they can
maintain relative predictability amidst the ever-increasing entropy around them
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?

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
(5). In simulated worlds,
such as video games, novelty-seeking intrinsic motivation can lead to
interesting and meaningful behavior. However, these environments may be
fundamentally lacking compared to the real world. In the real world, natural
forces and other agents offer bountiful novelty. Instead, the challenge in
natural environments is allostasis: discovering behaviors that enable agents to
maintain an equilibrium (homeostasis), for example to preserve their bodies,
their homes, and avoid predators and hunger. In the example below we shown an
example where an agent is experiencing random events due to the changing
weather. If the agent learns to build a shelter, in this case a house, the
agent will reduce the observed effects from weather.

We formalize homeostasis as an objective for reinforcement learning based on
surprise minimization (SMiRL). In entropic and dynamic environments with
undesirable forms of novelty, minimizing surprise (i.e., minimizing novelty)
causes agents to naturally seek an equilibrium that can be stably maintained.

Here we show an illustration of the agent interaction loop using SMiRL. When
the agent observes a state $mathbf{s}$, it computes the probability of this new state
given the belief the agent has $r_{t} leftarrow p_{theta_{t-1}}(textbf{s})$.
This belief models the states the agent is most familiar with – i.e., the
distribution of states it has seen in the past. Experiencing states that are
more familiar will result in higher reward. After the agent experience a new
state it updates its belief $p_{theta_{t-1}}(textbf{s})$ over states to
include the most recent experience. Then, the goal of the action policy
$pi(a|textbf{s}, theta_{t})$ is to choose actions that will result in the
agent consistently experiencing familiar states. Crucially, the agent
understands that its beliefs will change in the future. This means that it has
two mechanisms by which to maximize this reward: taking actions to visit
familiar states, and taking actions to visit states that will change its
such that future states are more familiar. It is this latter mechanism
that results in complex emergent behavior. Below, we visualize a policy trained
to play the game of Tetris. On the left the blocks the agent chooses are shown
and on the right is a visualization of $p_{theta_{t}}(textbf{s})$. We can see
how as the episode progresses the belief over possible locations to place
blocks tends to favor only the bottom row. This encourages the agent to
eliminate blocks to prevent board from filling up.


Tetris HauntedHouse


Left: Tetris. Right: HauntedHouse.

Emergent behavior

The SMiRL agent demonstrates meaningful emergent behaviors in a number of
different environments. In the Tetris environment, the agent is able to learn
proactive behaviors to eliminate rows and properly play the game. The agent
also learns emergent game playing behavior in the VizDoom environment,
acquiring an effective policy for dodging the fireballs thrown by the enemies.
In both of these environments, stochastic and chaotic events force the SMiRL
agent to take a coordinated course of action to avoid unusual states, such as
full Tetris boards or fireball explorations.

| Doom Hold The Line | Doom Defend The Line | HauntedHouse |
| ———————————————————— | ———————————————————— | :———————————————————-: |
| | | |

Doom Hold The Line Doom Defend The Line


Left: Doom Hold The Line. Right: Doom Defend The Line.


In the Cliff environment, the agent learns a policy that greatly reduces the
probability of falling off of the cliff by bracing against the ground and
stabilize itself at the edge, as shown in the figure below. In the Treadmill
environment, SMiRL learns a more complex locomotion behavior, jumping forward
to increase the time it stays on the treadmill, as shown in figure below.


Cliff Treadmill


Left: Cliff. Right: Treadmill.

Comparison to Intrinsic motivation:

Intrinsic motivation is the idea that behavior is driven by internal reward
signals that are task independent. Below, we show plots of the
environment-specific rewards over time on Tetris, VizDoomTakeCover, and the
humanoid domains. In order to compare SMiRL to more standard intrinsic
motivation methods, which seek out states that maximize surprise or novelty, we
also evaluated ICM (5) and
RND (6). We include an oracle agent
that directly optimizes the task reward. On Tetris, after training for $2000$
epochs, SMiRL achieves near perfect play, on par with the oracle reward
optimizing agent, with no deaths. ICM seeks novelty by creating more and more
distinct patterns of blocks rather than clearing them, leading to deteriorating
game scores over time. On VizDoomTakeCover, SmiRL effectively learns to dodge
fireballs thrown by the adversaries.

The baseline comparisons for the Cliff and Treadmill environments have a
similar outcome. The novelty seeking behavior of ICM causes it to learn a type
of irregular behavior that causes the agent to jump off the Cliff and roll
around on the Treadmill, maximizing the variety (and quantity) of falls.

SMiRL + Curiosity:

While on the surface, SMiRL minimizes surprise and curiosity approaches like
ICM maximize novelty, they are in fact not mutually incompatible. In
particular, while ICM maximizes novelty with respect to a learned transition
model, SMiRL minimizes surprise with respect to a learned state distribution.
We can combine ICM and SMiRL to achieve even better results on the Treadmill


Treadmill + ICM Pedestal


Left: Treadmill+ICM. Right: Pedestal.




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 is different from commonly proposed intrinsic exploration
methods based on novelty, which instead seek to visit novel states and increase
entropy. 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.