Infra-Bayesianism

Infra-Bayesianism is a new approach to epistemology /​ decision theory /​ reinforcement learning theory, which builds on “imprecise probability” to solve the problem of prior misspecification /​ grain-of-truth /​ nonrealizability which plagues Bayesianism and Bayesian reinforcement learning.

Infra-Bayesianism also naturally leads to an implementation of UDT, and (more speculatively at this stage) has applications to multi-agent theory, embedded agency and reflection. This sequence lays down the foundations of the approach.

In­tro­duc­tion To The In­fra-Bayesi­anism Sequence

Ba­sic In­framea­sure Theory

Belief Func­tions And De­ci­sion Theory

Less Ba­sic In­framea­sure Theory

In­framea­sures and Do­main Theory

The Many Faces of In­fra-Beliefs

Proofs Sec­tion 1.1 (Ini­tial re­sults to LF-du­al­ity)

Proofs Sec­tion 1.2 (Mix­tures, Up­dates, Push­for­wards)

Proofs Sec­tion 2.1 (The­o­rem 1, Lem­mas)

Proofs Sec­tion 2.2 (Iso­mor­phism to Ex­pec­ta­tions)

Proofs Sec­tion 2.3 (Up­dates, De­ci­sion The­ory)

LBIT Proofs 1: Propo­si­tions 1-9

LBIT Proofs 2: Propo­si­tions 10-18

LBIT Proofs 3: Propo­si­tions 19-22

LBIT Proofs 4: Propo­si­tions 22-28

LBIT Proofs 5: Propo­si­tions 29-38

LBIT Proofs 6: Propo­si­tions 39-47

LBIT Proofs 7: Propo­si­tions 48-52

LBIT Proofs 8: Propo­si­tions 53-58

In­fra-Do­main proofs 1

In­fra-Do­main Proofs 2