POMDPs

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This package provides a core interface for working with Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs). For examples, please see POMDPExamples, QuickPOMDPs, and the Gallery.

Our goal is to provide a common programming vocabulary for:

1. Expressing problems as MDPs and POMDPs.
2. Writing solver software.
3. Running simulations efficiently.

There are several ways to define (PO)MDPs:

• Transition and observation distributions and rewards can be defined separately with explicit or implicitly sampled distributions.
• All of the dynamics can be defined in a single generative model function: (s', o, r) = G(s,a).
• Problems may be defined with probability tables.
• The QuickPOMDPs interfaces make defining simple problems easier.

POMDPs.jl integrates with other ecosystems:

• The POMDPModelTools package provides two-way integration with CommonRLInterface and therefore with the JuliaReinforcementLearning packages.
• Python can be used to define and solve MDPs and POMDPs via the QuickPOMDPs or tabular interfaces and pyjulia (Example: tiger.py).

For help, please post in GitHub Discussions tab. We welcome contributions from anyone! See CONTRIBUTING.md for information about contributing.

Installation

POMDPs.jl and associated solver packages can be installed using Julia's package manager. For example, to install POMDPs.jl and the QMDP solver package, type the following in the Julia REPL:

using Pkg; Pkg.add("POMDPs"); Pkg.add("QMDP")

Some auxiliary packages and older versions of solvers may be found in the JuliaPOMDP registry. To install this registry, see the installation instructions.

Quick Start

To run a simple simulation of the classic Tiger POMDP using a policy created by the QMDP solver, you can use the following code (note that POMDPs.jl is not limited to discrete problems with explicitly-defined distributions like this):

using POMDPs, QuickPOMDPs, POMDPModelTools, POMDPSimulators, QMDP

m = QuickPOMDP(
    states = ["left", "right"],
    actions = ["left", "right", "listen"],
    observations = ["left", "right"],
    initialstate = Uniform(["left", "right"]),
    discount = 0.95,

    transition = function (s, a)
        if a == "listen"
            return Deterministic(s) # tiger stays behind the same door
        else # a door is opened
            return Uniform(["left", "right"]) # reset
        end
    end,

    observation = function (s, a, sp)
        if a == "listen"
            if sp == "left"
                return SparseCat(["left", "right"], [0.85, 0.15]) # sparse categorical distribution
            else
                return SparseCat(["right", "left"], [0.85, 0.15])
            end
        else
            return Uniform(["left", "right"])
        end
    end,

    reward = function (s, a)
        if a == "listen"
            return -1.0
        elseif s == a # the tiger was found
            return -100.0
        else # the tiger was escaped
            return 10.0
        end
    end
)

solver = QMDPSolver()
policy = solve(solver, m)

rsum = 0.0
for (s,b,a,o,r) in stepthrough(m, policy, "s,b,a,o,r", max_steps=10)
    println("s: $s, b: $([pdf(b,s) for s in states(m)]), a: $a, o: $o")
    global rsum += r
end
println("Undiscounted reward was $rsum.")

For more examples with visualization see POMDPGallery.jl.

Tutorials

Several tutorials are hosted in the POMDPExamples repository.

Documentation

Detailed documentation can be found here.

Supported Packages

Many packages use the POMDPs.jl interface, including MDP and POMDP solvers, support tools, and extensions to the POMDPs.jl interface. POMDPs.jl and all packages in the JuliaPOMDP project are fully supported on Linux and OS X. Windows is supported for all native solvers*, and most non-native solvers should work, but may require additional configuration.

Tools:

POMDPs.jl itself contains only the interface for communicating about problem definitions. Most of the functionality for interacting with problems is actually contained in several support tools packages:

Package	Build	Coverage
POMDPModelTools
BeliefUpdaters
POMDPPolicies
POMDPSimulators
POMDPModels
POMDPTesting
ParticleFilters
RLInterface

MDP solvers:

Package	Build/Coverage	Online/ Offline	Continuous States	Continuous Actions
Value Iteration		Offline	N	N
Local Approximation Value Iteration		Offline	Y	N
Global Approximation Value Iteration		Offline	Y	N
Monte Carlo Tree Search		Online	Y (DPW)	Y (DPW)

POMDP solvers:

Package	Build/Coverage	Online/ Offline	Continuous States	Continuous Actions	Continuous Observations
QMDP		Offline	N	N	N
FIB		Offline	N	N	N
BeliefGridValueIteration		Offline	N	N	N
SARSOP*		Offline	N	N	N
BasicPOMCP		Online	Y	N	N1
ARDESPOT		Online	Y	N	N1
MCVI		Offline	Y	N	Y
POMDPSolve*		Offline	N	N	N
IncrementalPruning		Offline	N	N	N
POMCPOW		Online	Y	Y2	Y
AEMS		Online	N	N	N
PointBasedValueIteration		Offline	N	N	N

¹: Will run, but will not converge to optimal solution

²: Will run, but convergence to optimal solution is not proven, and it will likely not work well on multidimensional action spaces

Reinforcement Learning:

Package	Build/Coverage	Continuous States	Continuous Actions
TabularTDLearning		N	N
DeepQLearning		Y1	N

¹: For POMDPs, it will use the observation instead of the state as input to the policy. See RLInterface.jl for more details.

Packages Awaiting Update

These packages were written for POMDPs.jl in Julia 0.6 and have not been updated to 1.0 yet.

Package	Build	Coverage
DESPOT

Performance Benchmarks:

*These packages require non-Julia dependencies

Citing POMDPs

If POMDPs is useful in your research and you would like to acknowledge it, please cite this paper:

@article{egorov2017pomdps,
  author  = {Maxim Egorov and Zachary N. Sunberg and Edward Balaban and Tim A. Wheeler and Jayesh K. Gupta and Mykel J. Kochenderfer},
  title   = {{POMDP}s.jl: A Framework for Sequential Decision Making under Uncertainty},
  journal = {Journal of Machine Learning Research},
  year    = {2017},
  volume  = {18},
  number  = {26},
  pages   = {1-5},
  url     = {http://jmlr.org/papers/v18/16-300.html}
}