Optimally solving decentralized decision-making problems modeled as Dec-POMDPs is known to be NEXP-complete. These optimal solutions are policies based on the entire history of observations and actions of an agent. However, some applications may require more compact policies because of limited compute capabilities, which can be modeled by considering a limited number of memory states (or agent states). While such an agent-state based policy class may not contain the optimal solution, it is still of practical interest to find the best agent-state policy within the class. We focus on an iterated best response style algorithm which guarantees monotonic improvements and convergence to a local optimum in polynomial runtime in the Dec-POMDP model size. In order to obtain a better local optimum, we use a modified objective which incentivizes risk-seeking alongside a conservative policy iteration update. Our empirical results show that our approach performs as well as state-of-the-art approaches on several benchmark Dec-POMDPs, achieving near-optimal performance while having polynomial runtime despite the limited memory. We also show that using more agent states (a larger memory) leads to greater performance. Our approach provides a novel way of incorporating memory constraints on the agents in the Dec-POMDP problem.
Figures & tables
T
FB-HSVI
PF-MAA ∗
RS-CPI (ours)
Dec Tiger
6
10.38
10.38
10.38
7
9.99
9.99
8.75
8
12.22
8.36
8.38
9
15.57
15.57
15.57
10
15.18
15.18
13.76
Table 1: Performance comparison across benchmarks and planning horizons T. RS-CPI uses ∣Zi∣=2 . The “-” entries were not not reported in the corresponding paper.
T
CPI only
RS only
No CPI + No RS
RS-CPI
Dec Tiger
6
10.38
−12.00
−12.00
10.38
7
8.75
−14.00
−14.00
8.75
8
6.50
−16.00
−16.00
8.38
9
10.10
−18.00
−18.00
15.57
10
8.42
−20.00
−20.00
13.76
Table 2: Ablations with risk-seeking and conservatism for the different planning horizons T . All experiments use ∣Zi∣=2 .
T
∣Zi∣=1
∣Zi∣=2
∣Zi∣=3
∣Zi∣=4
Dec Tiger
20
−31.77
27.63
31.58
30.69
50
−80.90
54.11
71.64
69.71
100
−123.01
120.30
145.14
152.04
Cooperative Box Pushing
20
448.09
469.39
472.97
474.25
Table 3: Table for comparison of number of agent states ∣Zi∣ with performance. We did not perform experiments for Mars Rovers for ∣Zi∣=4 .
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 1: Scaling of memory and runtime with horizon T and agent-state size Z across three benchmarks: Dec-Tiger, Cooperative Box Pushing, and Mars Rovers. Rows correspond to different metrics, columns correspond to Dec-POMDPs.
Figure 2: Cooperative Box Pushing (Image take from Seuken and Zilberstein (2012)
Time
Empty
Wall
OtherA
SmallB
LargeB
1
Forward Forward
TurnL TurnL
TurnL TurnL
TurnL TurnL
TurnL TurnL
2
TurnL Forward
TurnL TurnR
TurnL TurnR
Stay TurnL
TurnL TurnL
3
TurnL Forward
TurnL TurnR
TurnL TurnR
Forward TurnL
Forward Forward
4
TurnL Forward
TurnL TurnR
TurnL TurnR
Forward TurnL
Forward Forward
5
Forward Forward
TurnL TurnR
TurnL TurnR
Forward Forward
Forward Forward
6
Forward Forward
TurnL TurnR
TurnL TurnR
Stay Stay
Stay Stay
Appendix
Table 4: Cooperative Box Pushing : Joint policies over time. Top action in each cell: Agent 1 , bottom action: Agent 2 .
t
Pos1-NS
Pos2-NS
Pos3-NS
Pos4-NS
Pos1-S
Pos2-S
Pos3-S
Pos-S
1
SAMPLE RIGHT
UP UP
UP UP
UP UP
UP UP
UP UP
UP UP
UP UP
2
SAMPLE SAMPLE
SAMPLE UP
LEFT SAMPLE
UP UP
DOWN RIGHT
UP UP
UP UP
UP UP
3
SAMPLE RIGHT
SAMPLE SAMPLE
LEFT SAMPLE
LEFT UP
DOWN RIGHT
UP DOWN
LEFT DOWN
DOWN UP
4
SAMPLE SAMPLE
SAMPLE RIGHT
LEFT SAMPLE
LEFT SAMPLE
DOWN RIGHT
RIGHT RIGHT
LEFT DOWN
DOWN UP
5
DRILL DRILL
DOWN UP
UP DOWN
DOWN DOWN
DOWN RIGHT
RIGHT RIGHT
LEFT DOWN
UP DOWN
6
DOWN SAMPLE
SAMPLE RIGHT
SAMPLE SAMPLE
DRILL DRILL
DOWN RIGHT
SAMPLE RIGHT
SAMPLE DOWN
UP LEFT
Appendix
Table 5: Mars Rovers : Joint policies over time. Top action in each cell: Agent 1 , bottom action: Agent 2 .
University of Colorado Boulder, Boulder, Colorado, USA · Virginia Tech, Blacksburg, Virginia, USA · Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA